Illustrative Math Alignment: Grade 8 Unit 3
Linear Relationships
Lesson 5: Introduction to Linear Relationships
Use the following Media4Math resources with this Illustrative Math lesson.
| Thumbnail Image | Title | Body | Curriculum Topic |
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Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 16 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 16TopicLinear Functions DescriptionThis image shows a graph with two points (4, -8) and (4, -2). The example demonstrates how to find the equation of a vertical line passing through these points. The slope is undefined because division by zero occurs in calculating it. The slope formula is used: (y2 - y1) / (x2 - x1) = (-2 - (-8)) / (4 - 4) = 6 / 0 = undefined. Since this represents a vertical line, its equation is simply x = 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 16 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 16TopicLinear Functions DescriptionThis image shows a graph with two points (4, -8) and (4, -2). The example demonstrates how to find the equation of a vertical line passing through these points. The slope is undefined because division by zero occurs in calculating it. The slope formula is used: (y2 - y1) / (x2 - x1) = (-2 - (-8)) / (4 - 4) = 6 / 0 = undefined. Since this represents a vertical line, its equation is simply x = 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 16 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 16TopicLinear Functions DescriptionThis image shows a graph with two points (4, -8) and (4, -2). The example demonstrates how to find the equation of a vertical line passing through these points. The slope is undefined because division by zero occurs in calculating it. The slope formula is used: (y2 - y1) / (x2 - x1) = (-2 - (-8)) / (4 - 4) = 6 / 0 = undefined. Since this represents a vertical line, its equation is simply x = 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 16 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 16TopicLinear Functions DescriptionThis image shows a graph with two points (4, -8) and (4, -2). The example demonstrates how to find the equation of a vertical line passing through these points. The slope is undefined because division by zero occurs in calculating it. The slope formula is used: (y2 - y1) / (x2 - x1) = (-2 - (-8)) / (4 - 4) = 6 / 0 = undefined. Since this represents a vertical line, its equation is simply x = 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 16 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 16TopicLinear Functions DescriptionThis image shows a graph with two points (4, -8) and (4, -2). The example demonstrates how to find the equation of a vertical line passing through these points. The slope is undefined because division by zero occurs in calculating it. The slope formula is used: (y2 - y1) / (x2 - x1) = (-2 - (-8)) / (4 - 4) = 6 / 0 = undefined. Since this represents a vertical line, its equation is simply x = 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 17 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 17TopicLinear Functions DescriptionThis image shows a graph with two points plotted at (-2, 0.5) and (5, 4). The example demonstrates how to find the equation of a line using the slope formula and point-slope form. The slope is calculated as (4 - 0.5) / (5 - (-2)) = 3.5 / 7 = 1 / 2. The point-slope form is used to find the equation: y - 4 = (1 / 2)(x - 5), resulting in y = (1 / 2)x + 1 / 2. |
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 17 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 17TopicLinear Functions DescriptionThis image shows a graph with two points plotted at (-2, 0.5) and (5, 4). The example demonstrates how to find the equation of a line using the slope formula and point-slope form. The slope is calculated as (4 - 0.5) / (5 - (-2)) = 3.5 / 7 = 1 / 2. The point-slope form is used to find the equation: y - 4 = (1 / 2)(x - 5), resulting in y = (1 / 2)x + 1 / 2. |
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 17 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 17TopicLinear Functions DescriptionThis image shows a graph with two points plotted at (-2, 0.5) and (5, 4). The example demonstrates how to find the equation of a line using the slope formula and point-slope form. The slope is calculated as (4 - 0.5) / (5 - (-2)) = 3.5 / 7 = 1 / 2. The point-slope form is used to find the equation: y - 4 = (1 / 2)(x - 5), resulting in y = (1 / 2)x + 1 / 2. |
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 17 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 17TopicLinear Functions DescriptionThis image shows a graph with two points plotted at (-2, 0.5) and (5, 4). The example demonstrates how to find the equation of a line using the slope formula and point-slope form. The slope is calculated as (4 - 0.5) / (5 - (-2)) = 3.5 / 7 = 1 / 2. The point-slope form is used to find the equation: y - 4 = (1 / 2)(x - 5), resulting in y = (1 / 2)x + 1 / 2. |
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 17 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 17TopicLinear Functions DescriptionThis image shows a graph with two points plotted at (-2, 0.5) and (5, 4). The example demonstrates how to find the equation of a line using the slope formula and point-slope form. The slope is calculated as (4 - 0.5) / (5 - (-2)) = 3.5 / 7 = 1 / 2. The point-slope form is used to find the equation: y - 4 = (1 / 2)(x - 5), resulting in y = (1 / 2)x + 1 / 2. |
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 17 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 17TopicLinear Functions DescriptionThis image shows a graph with two points plotted at (-2, 0.5) and (5, 4). The example demonstrates how to find the equation of a line using the slope formula and point-slope form. The slope is calculated as (4 - 0.5) / (5 - (-2)) = 3.5 / 7 = 1 / 2. The point-slope form is used to find the equation: y - 4 = (1 / 2)(x - 5), resulting in y = (1 / 2)x + 1 / 2. |
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 18 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 18TopicLinear Functions DescriptionThis image shows a graph with two points plotted at (-3, 5) and (5, 1). The example demonstrates how to find the equation of a line using the slope formula and point-slope form. The slope is calculated as (5 - 1) / (-3 - 5) = -1 / 2. The point-slope form is used to find the equation: y - 5 = (-1 / 2)(x + 3), resulting in y = (-1 / 2)x + 7 / 2. |
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 18 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 18TopicLinear Functions DescriptionThis image shows a graph with two points plotted at (-3, 5) and (5, 1). The example demonstrates how to find the equation of a line using the slope formula and point-slope form. The slope is calculated as (5 - 1) / (-3 - 5) = -1 / 2. The point-slope form is used to find the equation: y - 5 = (-1 / 2)(x + 3), resulting in y = (-1 / 2)x + 7 / 2. |
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 18 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 18TopicLinear Functions DescriptionThis image shows a graph with two points plotted at (-3, 5) and (5, 1). The example demonstrates how to find the equation of a line using the slope formula and point-slope form. The slope is calculated as (5 - 1) / (-3 - 5) = -1 / 2. The point-slope form is used to find the equation: y - 5 = (-1 / 2)(x + 3), resulting in y = (-1 / 2)x + 7 / 2. |
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 18 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 18TopicLinear Functions DescriptionThis image shows a graph with two points plotted at (-3, 5) and (5, 1). The example demonstrates how to find the equation of a line using the slope formula and point-slope form. The slope is calculated as (5 - 1) / (-3 - 5) = -1 / 2. The point-slope form is used to find the equation: y - 5 = (-1 / 2)(x + 3), resulting in y = (-1 / 2)x + 7 / 2. |
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 18 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 18TopicLinear Functions DescriptionThis image shows a graph with two points plotted at (-3, 5) and (5, 1). The example demonstrates how to find the equation of a line using the slope formula and point-slope form. The slope is calculated as (5 - 1) / (-3 - 5) = -1 / 2. The point-slope form is used to find the equation: y - 5 = (-1 / 2)(x + 3), resulting in y = (-1 / 2)x + 7 / 2. |
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 18 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 18TopicLinear Functions DescriptionThis image shows a graph with two points plotted at (-3, 5) and (5, 1). The example demonstrates how to find the equation of a line using the slope formula and point-slope form. The slope is calculated as (5 - 1) / (-3 - 5) = -1 / 2. The point-slope form is used to find the equation: y - 5 = (-1 / 2)(x + 3), resulting in y = (-1 / 2)x + 7 / 2. |
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 19 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 19TopicLinear Functions DescriptionThis image shows a graph with two points plotted at (-4, 3) and (6, 3). The example demonstrates how to find the equation of a horizontal line using the slope formula and point-slope form. The slope is calculated as (3 - 3) / (-4 - 6) = 0. Since the slope is zero, the equation of the line is simply y = 3, indicating a horizontal line passing through y = 3. |
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 19 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 19TopicLinear Functions DescriptionThis image shows a graph with two points plotted at (-4, 3) and (6, 3). The example demonstrates how to find the equation of a horizontal line using the slope formula and point-slope form. The slope is calculated as (3 - 3) / (-4 - 6) = 0. Since the slope is zero, the equation of the line is simply y = 3, indicating a horizontal line passing through y = 3. |
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 19 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 19TopicLinear Functions DescriptionThis image shows a graph with two points plotted at (-4, 3) and (6, 3). The example demonstrates how to find the equation of a horizontal line using the slope formula and point-slope form. The slope is calculated as (3 - 3) / (-4 - 6) = 0. Since the slope is zero, the equation of the line is simply y = 3, indicating a horizontal line passing through y = 3. |
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 19 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 19TopicLinear Functions DescriptionThis image shows a graph with two points plotted at (-4, 3) and (6, 3). The example demonstrates how to find the equation of a horizontal line using the slope formula and point-slope form. The slope is calculated as (3 - 3) / (-4 - 6) = 0. Since the slope is zero, the equation of the line is simply y = 3, indicating a horizontal line passing through y = 3. |
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 19 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 19TopicLinear Functions DescriptionThis image shows a graph with two points plotted at (-4, 3) and (6, 3). The example demonstrates how to find the equation of a horizontal line using the slope formula and point-slope form. The slope is calculated as (3 - 3) / (-4 - 6) = 0. Since the slope is zero, the equation of the line is simply y = 3, indicating a horizontal line passing through y = 3. |
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 19 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 19TopicLinear Functions DescriptionThis image shows a graph with two points plotted at (-4, 3) and (6, 3). The example demonstrates how to find the equation of a horizontal line using the slope formula and point-slope form. The slope is calculated as (3 - 3) / (-4 - 6) = 0. Since the slope is zero, the equation of the line is simply y = 3, indicating a horizontal line passing through y = 3. |
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 2 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 2TopicLinear Functions DescriptionThis example illustrates the process of finding the equation of a line passing through the points (3, 7) and (9, 1). The slope is calculated as -1 using the formula (y2 - y1) / (x2 - x1). Employing the point-slope form, y - y1 = m(x - x1), the equation is derived as y - 1 = -(x - 9), which simplifies to y = -x + 10. |
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 2 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 2TopicLinear Functions DescriptionThis example illustrates the process of finding the equation of a line passing through the points (3, 7) and (9, 1). The slope is calculated as -1 using the formula (y2 - y1) / (x2 - x1). Employing the point-slope form, y - y1 = m(x - x1), the equation is derived as y - 1 = -(x - 9), which simplifies to y = -x + 10. |
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 2 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 2TopicLinear Functions DescriptionThis example illustrates the process of finding the equation of a line passing through the points (3, 7) and (9, 1). The slope is calculated as -1 using the formula (y2 - y1) / (x2 - x1). Employing the point-slope form, y - y1 = m(x - x1), the equation is derived as y - 1 = -(x - 9), which simplifies to y = -x + 10. |
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 2 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 2TopicLinear Functions DescriptionThis example illustrates the process of finding the equation of a line passing through the points (3, 7) and (9, 1). The slope is calculated as -1 using the formula (y2 - y1) / (x2 - x1). Employing the point-slope form, y - y1 = m(x - x1), the equation is derived as y - 1 = -(x - 9), which simplifies to y = -x + 10. |
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 2 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 2TopicLinear Functions DescriptionThis example illustrates the process of finding the equation of a line passing through the points (3, 7) and (9, 1). The slope is calculated as -1 using the formula (y2 - y1) / (x2 - x1). Employing the point-slope form, y - y1 = m(x - x1), the equation is derived as y - 1 = -(x - 9), which simplifies to y = -x + 10. |
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 2 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 2TopicLinear Functions DescriptionThis example illustrates the process of finding the equation of a line passing through the points (3, 7) and (9, 1). The slope is calculated as -1 using the formula (y2 - y1) / (x2 - x1). Employing the point-slope form, y - y1 = m(x - x1), the equation is derived as y - 1 = -(x - 9), which simplifies to y = -x + 10. |
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 20 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 20TopicLinear Functions DescriptionThis image shows a graph with two points plotted at (-3, -5) and (5, 1). The example demonstrates how to find the equation of a line using the slope formula and point-slope form. The slope is calculated as (1 - (-5)) / (5 - (-3)) = 6 / 8 = 3 / 4. The point-slope form is used to find the equation: y - 1 = (3 / 4)(x - 5), resulting in y = 3/4x - 2 3/4. |
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 20 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 20TopicLinear Functions DescriptionThis image shows a graph with two points plotted at (-3, -5) and (5, 1). The example demonstrates how to find the equation of a line using the slope formula and point-slope form. The slope is calculated as (1 - (-5)) / (5 - (-3)) = 6 / 8 = 3 / 4. The point-slope form is used to find the equation: y - 1 = (3 / 4)(x - 5), resulting in y = 3/4x - 2 3/4. |
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 20 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 20TopicLinear Functions DescriptionThis image shows a graph with two points plotted at (-3, -5) and (5, 1). The example demonstrates how to find the equation of a line using the slope formula and point-slope form. The slope is calculated as (1 - (-5)) / (5 - (-3)) = 6 / 8 = 3 / 4. The point-slope form is used to find the equation: y - 1 = (3 / 4)(x - 5), resulting in y = 3/4x - 2 3/4. |
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 20 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 20TopicLinear Functions DescriptionThis image shows a graph with two points plotted at (-3, -5) and (5, 1). The example demonstrates how to find the equation of a line using the slope formula and point-slope form. The slope is calculated as (1 - (-5)) / (5 - (-3)) = 6 / 8 = 3 / 4. The point-slope form is used to find the equation: y - 1 = (3 / 4)(x - 5), resulting in y = 3/4x - 2 3/4. |
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 20 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 20TopicLinear Functions DescriptionThis image shows a graph with two points plotted at (-3, -5) and (5, 1). The example demonstrates how to find the equation of a line using the slope formula and point-slope form. The slope is calculated as (1 - (-5)) / (5 - (-3)) = 6 / 8 = 3 / 4. The point-slope form is used to find the equation: y - 1 = (3 / 4)(x - 5), resulting in y = 3/4x - 2 3/4. |
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 20 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 20TopicLinear Functions DescriptionThis image shows a graph with two points plotted at (-3, -5) and (5, 1). The example demonstrates how to find the equation of a line using the slope formula and point-slope form. The slope is calculated as (1 - (-5)) / (5 - (-3)) = 6 / 8 = 3 / 4. The point-slope form is used to find the equation: y - 1 = (3 / 4)(x - 5), resulting in y = 3/4x - 2 3/4. |
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 21 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 21TopicLinear Functions DescriptionThe image shows a graph with two points (2, -4) and (6, 1) marked on a coordinate plane. The example demonstrates how to find the equation of a line using these two points. The slope is calculated using the slope formula, and then the point-slope form is applied to derive the equation of the line. The slope is calculated as (1 - (-4)) / (6 - 2) = 5 / 4. Using point-slope form: y - 1 = (5 / 4)(x - 6), which simplifies to y = 5/4x - 6 1/2. |
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 21 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 21TopicLinear Functions DescriptionThe image shows a graph with two points (2, -4) and (6, 1) marked on a coordinate plane. The example demonstrates how to find the equation of a line using these two points. The slope is calculated using the slope formula, and then the point-slope form is applied to derive the equation of the line. The slope is calculated as (1 - (-4)) / (6 - 2) = 5 / 4. Using point-slope form: y - 1 = (5 / 4)(x - 6), which simplifies to y = 5/4x - 6 1/2. |
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 21 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 21TopicLinear Functions DescriptionThe image shows a graph with two points (2, -4) and (6, 1) marked on a coordinate plane. The example demonstrates how to find the equation of a line using these two points. The slope is calculated using the slope formula, and then the point-slope form is applied to derive the equation of the line. The slope is calculated as (1 - (-4)) / (6 - 2) = 5 / 4. Using point-slope form: y - 1 = (5 / 4)(x - 6), which simplifies to y = 5/4x - 6 1/2. |
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 21 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 21TopicLinear Functions DescriptionThe image shows a graph with two points (2, -4) and (6, 1) marked on a coordinate plane. The example demonstrates how to find the equation of a line using these two points. The slope is calculated using the slope formula, and then the point-slope form is applied to derive the equation of the line. The slope is calculated as (1 - (-4)) / (6 - 2) = 5 / 4. Using point-slope form: y - 1 = (5 / 4)(x - 6), which simplifies to y = 5/4x - 6 1/2. |
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 21 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 21TopicLinear Functions DescriptionThe image shows a graph with two points (2, -4) and (6, 1) marked on a coordinate plane. The example demonstrates how to find the equation of a line using these two points. The slope is calculated using the slope formula, and then the point-slope form is applied to derive the equation of the line. The slope is calculated as (1 - (-4)) / (6 - 2) = 5 / 4. Using point-slope form: y - 1 = (5 / 4)(x - 6), which simplifies to y = 5/4x - 6 1/2. |
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 21 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 21TopicLinear Functions DescriptionThe image shows a graph with two points (2, -4) and (6, 1) marked on a coordinate plane. The example demonstrates how to find the equation of a line using these two points. The slope is calculated using the slope formula, and then the point-slope form is applied to derive the equation of the line. The slope is calculated as (1 - (-4)) / (6 - 2) = 5 / 4. Using point-slope form: y - 1 = (5 / 4)(x - 6), which simplifies to y = 5/4x - 6 1/2. |
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 22 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 22TopicLinear Functions DescriptionThe image shows a graph with two points (5, 1) and (8, -5) marked on a coordinate plane. The example demonstrates how to find the equation of a line using these two points. The slope is calculated using the slope formula, and then the point-slope form is applied to derive the equation of the line. The slope is calculated as (1 - (-5)) / (5 - 8) = -2. Using point-slope form: y - 1 = -2(x - 5), which simplifies to y = -2x + 11. |
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 22 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 22TopicLinear Functions DescriptionThe image shows a graph with two points (5, 1) and (8, -5) marked on a coordinate plane. The example demonstrates how to find the equation of a line using these two points. The slope is calculated using the slope formula, and then the point-slope form is applied to derive the equation of the line. The slope is calculated as (1 - (-5)) / (5 - 8) = -2. Using point-slope form: y - 1 = -2(x - 5), which simplifies to y = -2x + 11. |
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 22 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 22TopicLinear Functions DescriptionThe image shows a graph with two points (5, 1) and (8, -5) marked on a coordinate plane. The example demonstrates how to find the equation of a line using these two points. The slope is calculated using the slope formula, and then the point-slope form is applied to derive the equation of the line. The slope is calculated as (1 - (-5)) / (5 - 8) = -2. Using point-slope form: y - 1 = -2(x - 5), which simplifies to y = -2x + 11. |
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 22 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 22TopicLinear Functions DescriptionThe image shows a graph with two points (5, 1) and (8, -5) marked on a coordinate plane. The example demonstrates how to find the equation of a line using these two points. The slope is calculated using the slope formula, and then the point-slope form is applied to derive the equation of the line. The slope is calculated as (1 - (-5)) / (5 - 8) = -2. Using point-slope form: y - 1 = -2(x - 5), which simplifies to y = -2x + 11. |
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 22 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 22TopicLinear Functions DescriptionThe image shows a graph with two points (5, 1) and (8, -5) marked on a coordinate plane. The example demonstrates how to find the equation of a line using these two points. The slope is calculated using the slope formula, and then the point-slope form is applied to derive the equation of the line. The slope is calculated as (1 - (-5)) / (5 - 8) = -2. Using point-slope form: y - 1 = -2(x - 5), which simplifies to y = -2x + 11. |
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 22 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 22TopicLinear Functions DescriptionThe image shows a graph with two points (5, 1) and (8, -5) marked on a coordinate plane. The example demonstrates how to find the equation of a line using these two points. The slope is calculated using the slope formula, and then the point-slope form is applied to derive the equation of the line. The slope is calculated as (1 - (-5)) / (5 - 8) = -2. Using point-slope form: y - 1 = -2(x - 5), which simplifies to y = -2x + 11. |
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 23 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 23TopicLinear Functions DescriptionThe image shows a graph with two points (6, 1) and (6, -5) marked on a coordinate plane. The example demonstrates how to find the equation of a vertical line using these two points. Since both x-coordinates are equal, the slope is undefined, indicating a vertical line. The slope is undefined because x-values are equal: (1 - (-5)) / (6 - 6) = undefined. This means it's a vertical line at x = 6. |
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 23 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 23TopicLinear Functions DescriptionThe image shows a graph with two points (6, 1) and (6, -5) marked on a coordinate plane. The example demonstrates how to find the equation of a vertical line using these two points. Since both x-coordinates are equal, the slope is undefined, indicating a vertical line. The slope is undefined because x-values are equal: (1 - (-5)) / (6 - 6) = undefined. This means it's a vertical line at x = 6. |
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 23 | Math Example--Linear Function Concepts--The Equation of a Line Given Two Points: Example 23TopicLinear Functions DescriptionThe image shows a graph with two points (6, 1) and (6, -5) marked on a coordinate plane. The example demonstrates how to find the equation of a vertical line using these two points. Since both x-coordinates are equal, the slope is undefined, indicating a vertical line. The slope is undefined because x-values are equal: (1 - (-5)) / (6 - 6) = undefined. This means it's a vertical line at x = 6. |
Point-Slope Form and Slope-Intercept Form |
