Illustrative Math Alignment: Grade 8 Unit 3
Linear Relationships
Lesson 3: Representing Proportional Relationships
Use the following Media4Math resources with this Illustrative Math lesson.
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Math Example--Coordinate Geometry--Slope Formula: Example 17 | Math Example--Coordinate Geometry--Slope Formula: Example 17TopicSlope Formula DescriptionThis example illustrates the calculation of slope for a horizontal line connecting points (-2, -7) and (3, -7) on a Cartesian plane. When we apply the slope formula, we find that the slope is (-7 - (-7)) / (-2 - 3) = 0 / -5 = 0. The slope formula is a key concept in coordinate geometry, helping us understand the steepness and direction of lines. This particular example highlights a special case where the line is horizontal, resulting in a slope of zero, even when the points have different x-coordinates. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 18 | Math Example--Coordinate Geometry--Slope Formula: Example 18TopicSlope Formula DescriptionThis example demonstrates the calculation of slope for a line connecting two points: (-6, 0) and (0, 4) on a Cartesian plane. Applying the slope formula, we find that the slope is (4 - 0) / (0 - (-6)) = 4 / 6 = 2 / 3. The slope formula is a fundamental concept in coordinate geometry, helping us understand the steepness and direction of lines. This example shows how to handle points with both positive and negative coordinates when calculating slope, resulting in a positive fraction. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 18 | Math Example--Coordinate Geometry--Slope Formula: Example 18TopicSlope Formula DescriptionThis example demonstrates the calculation of slope for a line connecting two points: (-6, 0) and (0, 4) on a Cartesian plane. Applying the slope formula, we find that the slope is (4 - 0) / (0 - (-6)) = 4 / 6 = 2 / 3. The slope formula is a fundamental concept in coordinate geometry, helping us understand the steepness and direction of lines. This example shows how to handle points with both positive and negative coordinates when calculating slope, resulting in a positive fraction. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 18 | Math Example--Coordinate Geometry--Slope Formula: Example 18TopicSlope Formula DescriptionThis example demonstrates the calculation of slope for a line connecting two points: (-6, 0) and (0, 4) on a Cartesian plane. Applying the slope formula, we find that the slope is (4 - 0) / (0 - (-6)) = 4 / 6 = 2 / 3. The slope formula is a fundamental concept in coordinate geometry, helping us understand the steepness and direction of lines. This example shows how to handle points with both positive and negative coordinates when calculating slope, resulting in a positive fraction. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 19 | Math Example--Coordinate Geometry--Slope Formula: Example 19TopicSlope Formula DescriptionThis example illustrates the calculation of slope for a line connecting two points: (1, 0) and (0, 6) on a Cartesian plane. Applying the slope formula, we find that the slope is (6 - 0) / (0 - 1) = 6 / -1 = -6. The slope formula is a crucial concept in coordinate geometry, helping us understand the steepness and direction of lines. This example demonstrates how to handle points with both positive and negative coordinates when calculating slope, resulting in a negative integer slope. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 19 | Math Example--Coordinate Geometry--Slope Formula: Example 19TopicSlope Formula DescriptionThis example illustrates the calculation of slope for a line connecting two points: (1, 0) and (0, 6) on a Cartesian plane. Applying the slope formula, we find that the slope is (6 - 0) / (0 - 1) = 6 / -1 = -6. The slope formula is a crucial concept in coordinate geometry, helping us understand the steepness and direction of lines. This example demonstrates how to handle points with both positive and negative coordinates when calculating slope, resulting in a negative integer slope. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 19 | Math Example--Coordinate Geometry--Slope Formula: Example 19TopicSlope Formula DescriptionThis example illustrates the calculation of slope for a line connecting two points: (1, 0) and (0, 6) on a Cartesian plane. Applying the slope formula, we find that the slope is (6 - 0) / (0 - 1) = 6 / -1 = -6. The slope formula is a crucial concept in coordinate geometry, helping us understand the steepness and direction of lines. This example demonstrates how to handle points with both positive and negative coordinates when calculating slope, resulting in a negative integer slope. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 2 | Math Example--Coordinate Geometry--Slope Formula: Example 2TopicSlope Formula DescriptionThis example illustrates the calculation of slope between two points (3, 7) and (9, 2) on a coordinate grid. The slope formula is applied to find that the slope is (7 - 2) / (3 - 9) = 5 / -6 = -5 / 6. Understanding the slope formula is crucial in coordinate geometry as it helps describe the steepness and direction of a line. This concept is widely used in various mathematical applications and real-world scenarios. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 2 | Math Example--Coordinate Geometry--Slope Formula: Example 2TopicSlope Formula DescriptionThis example illustrates the calculation of slope between two points (3, 7) and (9, 2) on a coordinate grid. The slope formula is applied to find that the slope is (7 - 2) / (3 - 9) = 5 / -6 = -5 / 6. Understanding the slope formula is crucial in coordinate geometry as it helps describe the steepness and direction of a line. This concept is widely used in various mathematical applications and real-world scenarios. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 2 | Math Example--Coordinate Geometry--Slope Formula: Example 2TopicSlope Formula DescriptionThis example illustrates the calculation of slope between two points (3, 7) and (9, 2) on a coordinate grid. The slope formula is applied to find that the slope is (7 - 2) / (3 - 9) = 5 / -6 = -5 / 6. Understanding the slope formula is crucial in coordinate geometry as it helps describe the steepness and direction of a line. This concept is widely used in various mathematical applications and real-world scenarios. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 20 | Math Example--Coordinate Geometry--Slope Formula: Example 20TopicSlope Formula DescriptionThis example demonstrates the calculation of slope for a horizontal line connecting points (0, 0) and (8, 0) on a Cartesian plane. When we apply the slope formula, we find that the slope is (0 - 0) / (8 - 0) = 0 / 8 = 0. The slope formula is a key concept in coordinate geometry, helping us understand the steepness and direction of lines. This particular example highlights a special case where the line is horizontal and lies on the x-axis, resulting in a slope of zero. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 20 | Math Example--Coordinate Geometry--Slope Formula: Example 20TopicSlope Formula DescriptionThis example demonstrates the calculation of slope for a horizontal line connecting points (0, 0) and (8, 0) on a Cartesian plane. When we apply the slope formula, we find that the slope is (0 - 0) / (8 - 0) = 0 / 8 = 0. The slope formula is a key concept in coordinate geometry, helping us understand the steepness and direction of lines. This particular example highlights a special case where the line is horizontal and lies on the x-axis, resulting in a slope of zero. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 20 | Math Example--Coordinate Geometry--Slope Formula: Example 20TopicSlope Formula DescriptionThis example demonstrates the calculation of slope for a horizontal line connecting points (0, 0) and (8, 0) on a Cartesian plane. When we apply the slope formula, we find that the slope is (0 - 0) / (8 - 0) = 0 / 8 = 0. The slope formula is a key concept in coordinate geometry, helping us understand the steepness and direction of lines. This particular example highlights a special case where the line is horizontal and lies on the x-axis, resulting in a slope of zero. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 21 | Math Example--Coordinate Geometry--Slope Formula: Example 21TopicSlope Formula DescriptionThis example illustrates the calculation of slope for a vertical line connecting points (0, 0) and (0, 6) on a Cartesian plane. When we apply the slope formula, we find that the slope is (6 - 0) / (0 - 0) = 6 / 0, which is undefined. The slope formula is a fundamental concept in coordinate geometry, helping us understand the steepness and direction of lines. This particular example highlights a special case where the line is vertical and lies on the y-axis, resulting in an undefined slope due to division by zero. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 21 | Math Example--Coordinate Geometry--Slope Formula: Example 21TopicSlope Formula DescriptionThis example illustrates the calculation of slope for a vertical line connecting points (0, 0) and (0, 6) on a Cartesian plane. When we apply the slope formula, we find that the slope is (6 - 0) / (0 - 0) = 6 / 0, which is undefined. The slope formula is a fundamental concept in coordinate geometry, helping us understand the steepness and direction of lines. This particular example highlights a special case where the line is vertical and lies on the y-axis, resulting in an undefined slope due to division by zero. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 21 | Math Example--Coordinate Geometry--Slope Formula: Example 21TopicSlope Formula DescriptionThis example illustrates the calculation of slope for a vertical line connecting points (0, 0) and (0, 6) on a Cartesian plane. When we apply the slope formula, we find that the slope is (6 - 0) / (0 - 0) = 6 / 0, which is undefined. The slope formula is a fundamental concept in coordinate geometry, helping us understand the steepness and direction of lines. This particular example highlights a special case where the line is vertical and lies on the y-axis, resulting in an undefined slope due to division by zero. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 3 | Math Example--Coordinate Geometry--Slope Formula: Example 3TopicSlope Formula DescriptionThis example demonstrates the calculation of slope for a horizontal line connecting points (2, 4) and (9, 4) on a coordinate grid. When we apply the slope formula, we find that the slope is (4 - 4) / (9 - 2) = 0 / 7 = 0. The slope formula is a fundamental concept in coordinate geometry, helping us understand the steepness and direction of lines. This particular example highlights a special case where the line is horizontal, resulting in a slope of zero. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 3 | Math Example--Coordinate Geometry--Slope Formula: Example 3TopicSlope Formula DescriptionThis example demonstrates the calculation of slope for a horizontal line connecting points (2, 4) and (9, 4) on a coordinate grid. When we apply the slope formula, we find that the slope is (4 - 4) / (9 - 2) = 0 / 7 = 0. The slope formula is a fundamental concept in coordinate geometry, helping us understand the steepness and direction of lines. This particular example highlights a special case where the line is horizontal, resulting in a slope of zero. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 3 | Math Example--Coordinate Geometry--Slope Formula: Example 3TopicSlope Formula DescriptionThis example demonstrates the calculation of slope for a horizontal line connecting points (2, 4) and (9, 4) on a coordinate grid. When we apply the slope formula, we find that the slope is (4 - 4) / (9 - 2) = 0 / 7 = 0. The slope formula is a fundamental concept in coordinate geometry, helping us understand the steepness and direction of lines. This particular example highlights a special case where the line is horizontal, resulting in a slope of zero. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 4 | Math Example--Coordinate Geometry--Slope Formula: Example 4TopicSlope Formula DescriptionThis example illustrates the calculation of slope for a vertical line passing through points (5, 8) and (5, 2) on a coordinate grid. When we apply the slope formula, we find that the slope is (8 - 2) / (5 - 5) = 6 / 0, which is undefined. The slope formula is a key concept in coordinate geometry, helping us understand the steepness and direction of lines. This particular example highlights a special case where the line is vertical, resulting in an undefined slope. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 4 | Math Example--Coordinate Geometry--Slope Formula: Example 4TopicSlope Formula DescriptionThis example illustrates the calculation of slope for a vertical line passing through points (5, 8) and (5, 2) on a coordinate grid. When we apply the slope formula, we find that the slope is (8 - 2) / (5 - 5) = 6 / 0, which is undefined. The slope formula is a key concept in coordinate geometry, helping us understand the steepness and direction of lines. This particular example highlights a special case where the line is vertical, resulting in an undefined slope. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 4 | Math Example--Coordinate Geometry--Slope Formula: Example 4TopicSlope Formula DescriptionThis example illustrates the calculation of slope for a vertical line passing through points (5, 8) and (5, 2) on a coordinate grid. When we apply the slope formula, we find that the slope is (8 - 2) / (5 - 5) = 6 / 0, which is undefined. The slope formula is a key concept in coordinate geometry, helping us understand the steepness and direction of lines. This particular example highlights a special case where the line is vertical, resulting in an undefined slope. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 5 | Math Example--Coordinate Geometry--Slope Formula: Example 5TopicSlope Formula DescriptionThis example demonstrates the calculation of slope for a line connecting two points in different quadrants: (-6, -2) in Quadrant III and (6, 5) in Quadrant I. Applying the slope formula, we find that the slope is (5 - (-2)) / (6 - (-6)) = 7 / 12 = 1 / 4. The slope formula is a crucial concept in coordinate geometry, helping us understand the steepness and direction of lines. This example shows how to handle negative coordinates and points in different quadrants when calculating slope. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 5 | Math Example--Coordinate Geometry--Slope Formula: Example 5TopicSlope Formula DescriptionThis example demonstrates the calculation of slope for a line connecting two points in different quadrants: (-6, -2) in Quadrant III and (6, 5) in Quadrant I. Applying the slope formula, we find that the slope is (5 - (-2)) / (6 - (-6)) = 7 / 12 = 1 / 4. The slope formula is a crucial concept in coordinate geometry, helping us understand the steepness and direction of lines. This example shows how to handle negative coordinates and points in different quadrants when calculating slope. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 5 | Math Example--Coordinate Geometry--Slope Formula: Example 5TopicSlope Formula DescriptionThis example demonstrates the calculation of slope for a line connecting two points in different quadrants: (-6, -2) in Quadrant III and (6, 5) in Quadrant I. Applying the slope formula, we find that the slope is (5 - (-2)) / (6 - (-6)) = 7 / 12 = 1 / 4. The slope formula is a crucial concept in coordinate geometry, helping us understand the steepness and direction of lines. This example shows how to handle negative coordinates and points in different quadrants when calculating slope. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 6 | Math Example--Coordinate Geometry--Slope Formula: Example 6TopicSlope Formula DescriptionThis example illustrates the calculation of slope for a line connecting two points in different quadrants: (-4, 8) in Quadrant II and (6, 2) in Quadrant I. Applying the slope formula, we find that the slope is (8 - 2) / (-4 - 6) = 6 / -10 = -3 / 5. The slope formula is a fundamental concept in coordinate geometry, helping us understand the steepness and direction of lines. This example demonstrates how to handle points in different quadrants and interpret a negative slope. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 6 | Math Example--Coordinate Geometry--Slope Formula: Example 6TopicSlope Formula DescriptionThis example illustrates the calculation of slope for a line connecting two points in different quadrants: (-4, 8) in Quadrant II and (6, 2) in Quadrant I. Applying the slope formula, we find that the slope is (8 - 2) / (-4 - 6) = 6 / -10 = -3 / 5. The slope formula is a fundamental concept in coordinate geometry, helping us understand the steepness and direction of lines. This example demonstrates how to handle points in different quadrants and interpret a negative slope. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 6 | Math Example--Coordinate Geometry--Slope Formula: Example 6TopicSlope Formula DescriptionThis example illustrates the calculation of slope for a line connecting two points in different quadrants: (-4, 8) in Quadrant II and (6, 2) in Quadrant I. Applying the slope formula, we find that the slope is (8 - 2) / (-4 - 6) = 6 / -10 = -3 / 5. The slope formula is a fundamental concept in coordinate geometry, helping us understand the steepness and direction of lines. This example demonstrates how to handle points in different quadrants and interpret a negative slope. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 7 | Math Example--Coordinate Geometry--Slope Formula: Example 7TopicSlope Formula DescriptionThis example demonstrates the calculation of slope for a horizontal line connecting two points: (-4, 3) in Quadrant II and (2, 3) in Quadrant I. When we apply the slope formula, we find that the slope is (3 - 3) / (-4 - 2) = 0 / -6 = 0. The slope formula is a key concept in coordinate geometry, helping us understand the steepness and direction of lines. This particular example highlights a special case where the line is horizontal, resulting in a slope of zero, even when the points are in different quadrants. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 7 | Math Example--Coordinate Geometry--Slope Formula: Example 7TopicSlope Formula DescriptionThis example demonstrates the calculation of slope for a horizontal line connecting two points: (-4, 3) in Quadrant II and (2, 3) in Quadrant I. When we apply the slope formula, we find that the slope is (3 - 3) / (-4 - 2) = 0 / -6 = 0. The slope formula is a key concept in coordinate geometry, helping us understand the steepness and direction of lines. This particular example highlights a special case where the line is horizontal, resulting in a slope of zero, even when the points are in different quadrants. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 7 | Math Example--Coordinate Geometry--Slope Formula: Example 7TopicSlope Formula DescriptionThis example demonstrates the calculation of slope for a horizontal line connecting two points: (-4, 3) in Quadrant II and (2, 3) in Quadrant I. When we apply the slope formula, we find that the slope is (3 - 3) / (-4 - 2) = 0 / -6 = 0. The slope formula is a key concept in coordinate geometry, helping us understand the steepness and direction of lines. This particular example highlights a special case where the line is horizontal, resulting in a slope of zero, even when the points are in different quadrants. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 8 | Math Example--Coordinate Geometry--Slope Formula: Example 8TopicSlope Formula DescriptionThis example illustrates the calculation of slope for a line connecting two points in different quadrants: (-2, -8) in Quadrant III and (6, 2) in Quadrant I. Applying the slope formula, we find that the slope is (2 - (-8)) / (6 - (-2)) = 10 / 8 = 5 / 4. The slope formula is a crucial concept in coordinate geometry, helping us understand the steepness and direction of lines. This example shows how to handle negative coordinates and points in different quadrants when calculating slope. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 8 | Math Example--Coordinate Geometry--Slope Formula: Example 8TopicSlope Formula DescriptionThis example illustrates the calculation of slope for a line connecting two points in different quadrants: (-2, -8) in Quadrant III and (6, 2) in Quadrant I. Applying the slope formula, we find that the slope is (2 - (-8)) / (6 - (-2)) = 10 / 8 = 5 / 4. The slope formula is a crucial concept in coordinate geometry, helping us understand the steepness and direction of lines. This example shows how to handle negative coordinates and points in different quadrants when calculating slope. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 8 | Math Example--Coordinate Geometry--Slope Formula: Example 8TopicSlope Formula DescriptionThis example illustrates the calculation of slope for a line connecting two points in different quadrants: (-2, -8) in Quadrant III and (6, 2) in Quadrant I. Applying the slope formula, we find that the slope is (2 - (-8)) / (6 - (-2)) = 10 / 8 = 5 / 4. The slope formula is a crucial concept in coordinate geometry, helping us understand the steepness and direction of lines. This example shows how to handle negative coordinates and points in different quadrants when calculating slope. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 9 | Math Example--Coordinate Geometry--Slope Formula: Example 9TopicSlope Formula DescriptionThis example demonstrates the calculation of slope for a line connecting two points: (9, 6) and (2, -8) on a Cartesian plane. Applying the slope formula, we find that the slope is (6 - (-8)) / (9 - 2) = 14 / 7 = 2. The slope formula is a fundamental concept in coordinate geometry, helping us understand the steepness and direction of lines. This example shows how to handle points with both positive and negative coordinates when calculating slope. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 9 | Math Example--Coordinate Geometry--Slope Formula: Example 9TopicSlope Formula DescriptionThis example demonstrates the calculation of slope for a line connecting two points: (9, 6) and (2, -8) on a Cartesian plane. Applying the slope formula, we find that the slope is (6 - (-8)) / (9 - 2) = 14 / 7 = 2. The slope formula is a fundamental concept in coordinate geometry, helping us understand the steepness and direction of lines. This example shows how to handle points with both positive and negative coordinates when calculating slope. |
Slope |
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Math Example--Coordinate Geometry--Slope Formula: Example 9 | Math Example--Coordinate Geometry--Slope Formula: Example 9TopicSlope Formula DescriptionThis example demonstrates the calculation of slope for a line connecting two points: (9, 6) and (2, -8) on a Cartesian plane. Applying the slope formula, we find that the slope is (6 - (-8)) / (9 - 2) = 14 / 7 = 2. The slope formula is a fundamental concept in coordinate geometry, helping us understand the steepness and direction of lines. This example shows how to handle points with both positive and negative coordinates when calculating slope. |
Slope |
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Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 1 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 1TopicLinear Functions DescriptionThis example demonstrates how to find the equation of a line passing through two given points: (6, 4) and (8, 8). The slope is calculated using the formula (y2 - y1) / (x2 - x1), resulting in a slope of 2. Using the point-slope form of a line, y - y1 = m(x - x1), the equation is derived as y - 8 = 2(x - 8), which simplifies to y = 2x - 8. |
Point-Slope Form and Slope-Intercept Form |
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Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 1 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 1TopicLinear Functions DescriptionThis example demonstrates how to find the equation of a line passing through two given points: (6, 4) and (8, 8). The slope is calculated using the formula (y2 - y1) / (x2 - x1), resulting in a slope of 2. Using the point-slope form of a line, y - y1 = m(x - x1), the equation is derived as y - 8 = 2(x - 8), which simplifies to y = 2x - 8. |
Point-Slope Form and Slope-Intercept Form |
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Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 1 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 1TopicLinear Functions DescriptionThis example demonstrates how to find the equation of a line passing through two given points: (6, 4) and (8, 8). The slope is calculated using the formula (y2 - y1) / (x2 - x1), resulting in a slope of 2. Using the point-slope form of a line, y - y1 = m(x - x1), the equation is derived as y - 8 = 2(x - 8), which simplifies to y = 2x - 8. |
Point-Slope Form and Slope-Intercept Form |
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Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 10 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 10TopicLinear Functions DescriptionThe image shows a coordinate plane with two points (-6, -2) and (-2, -6) marked. It provides a step-by-step solution to find the equation of the line passing through these points. The slope is calculated, and the equation is derived using point-slope form. The slope is calculated as (y2 - y1) / (x2 - x1) = (-6 - (-2)) / (-2 - (-6)) = -4 / 4 = -1. Using point-slope form, y - y1 = m(x - x1), the equation is derived as y + 2 = -(x + 6), which simplifies to y = -x - 8. |
Point-Slope Form and Slope-Intercept Form |
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Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 10 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 10TopicLinear Functions DescriptionThe image shows a coordinate plane with two points (-6, -2) and (-2, -6) marked. It provides a step-by-step solution to find the equation of the line passing through these points. The slope is calculated, and the equation is derived using point-slope form. The slope is calculated as (y2 - y1) / (x2 - x1) = (-6 - (-2)) / (-2 - (-6)) = -4 / 4 = -1. Using point-slope form, y - y1 = m(x - x1), the equation is derived as y + 2 = -(x + 6), which simplifies to y = -x - 8. |
Point-Slope Form and Slope-Intercept Form |
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Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 10 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 10TopicLinear Functions DescriptionThe image shows a coordinate plane with two points (-6, -2) and (-2, -6) marked. It provides a step-by-step solution to find the equation of the line passing through these points. The slope is calculated, and the equation is derived using point-slope form. The slope is calculated as (y2 - y1) / (x2 - x1) = (-6 - (-2)) / (-2 - (-6)) = -4 / 4 = -1. Using point-slope form, y - y1 = m(x - x1), the equation is derived as y + 2 = -(x + 6), which simplifies to y = -x - 8. |
Point-Slope Form and Slope-Intercept Form |
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Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 11 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 11TopicLinear Functions DescriptionThe image shows a coordinate plane with two points (-8, -4) and (-2, -4) marked. It provides a step-by-step solution to find the equation of the line passing through these points. The slope is calculated as zero, indicating a horizontal line. The slope is calculated as (y2 - y1) / (x2 - x1) = (-4 - (-4)) / (-8 - (-2)) = 0 / -6 = 0. Since the slope is zero, it indicates a horizontal line at y = -4. Using point-slope form, the equation becomes y + 4 = 0, which simplifies to y = -4. |
Point-Slope Form and Slope-Intercept Form |
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Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 11 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 11TopicLinear Functions DescriptionThe image shows a coordinate plane with two points (-8, -4) and (-2, -4) marked. It provides a step-by-step solution to find the equation of the line passing through these points. The slope is calculated as zero, indicating a horizontal line. The slope is calculated as (y2 - y1) / (x2 - x1) = (-4 - (-4)) / (-8 - (-2)) = 0 / -6 = 0. Since the slope is zero, it indicates a horizontal line at y = -4. Using point-slope form, the equation becomes y + 4 = 0, which simplifies to y = -4. |
Point-Slope Form and Slope-Intercept Form |
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Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 11 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 11TopicLinear Functions DescriptionThe image shows a coordinate plane with two points (-8, -4) and (-2, -4) marked. It provides a step-by-step solution to find the equation of the line passing through these points. The slope is calculated as zero, indicating a horizontal line. The slope is calculated as (y2 - y1) / (x2 - x1) = (-4 - (-4)) / (-8 - (-2)) = 0 / -6 = 0. Since the slope is zero, it indicates a horizontal line at y = -4. Using point-slope form, the equation becomes y + 4 = 0, which simplifies to y = -4. |
Point-Slope Form and Slope-Intercept Form |
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Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 12 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 12TopicLinear Functions DescriptionThe image shows a coordinate plane with two points (-5, -8) and (-5, -3) marked. It provides a step-by-step solution to find the equation of the line passing through these points. The slope is undefined, indicating a vertical line. The slope is calculated as (y2 - y1) / (x2 - x1) = (-3 - (-8)) / (-5 - (-5)) = 5 / 0, which is undefined. Since the slope is undefined, it indicates a vertical line at x = -5. Therefore, the equation of the line is simply x = -5. |
Point-Slope Form and Slope-Intercept Form |
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Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 12 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 12TopicLinear Functions DescriptionThe image shows a coordinate plane with two points (-5, -8) and (-5, -3) marked. It provides a step-by-step solution to find the equation of the line passing through these points. The slope is undefined, indicating a vertical line. The slope is calculated as (y2 - y1) / (x2 - x1) = (-3 - (-8)) / (-5 - (-5)) = 5 / 0, which is undefined. Since the slope is undefined, it indicates a vertical line at x = -5. Therefore, the equation of the line is simply x = -5. |
Point-Slope Form and Slope-Intercept Form |
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Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 12 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 12TopicLinear Functions DescriptionThe image shows a coordinate plane with two points (-5, -8) and (-5, -3) marked. It provides a step-by-step solution to find the equation of the line passing through these points. The slope is undefined, indicating a vertical line. The slope is calculated as (y2 - y1) / (x2 - x1) = (-3 - (-8)) / (-5 - (-5)) = 5 / 0, which is undefined. Since the slope is undefined, it indicates a vertical line at x = -5. Therefore, the equation of the line is simply x = -5. |
Point-Slope Form and Slope-Intercept Form |
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Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 13 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 13TopicLinear Functions DescriptionThis image shows a graph with two points (2, -4) and (6, -2) marked. The example demonstrates how to find the equation of a line passing through these points. The slope is calculated as 1/2, and the point-slope form is used to derive the equation of the line. The slope formula is used: (y2 - y1) / (x2 - x1) = (-2 - (-4)) / (6 - 2) = 2 / 4 = 1/2. Then, using the point-slope form: y - (-2) = (1/2)(x - 6), which simplifies to y = (1/2)x - 5. |
Point-Slope Form and Slope-Intercept Form |
