Illustrative Math Alignment: Grade 8 Unit 3

In these clip art images, show students the difference between ratios and rates. These images are useful when talking about slope as both a ratio and a rate. In particular, this is useful when talking about slope as a rate of change.

Have students compare the slopes of the pairs of lines from these clip art images. Have them use the background grid for measuring the rise and the run.

In this set of clip art images, different values for the rise and run are given, but in all cases they result in the same slope for the staircase. These images help advance the idea that slope is a ratio and proportion.

In this set of clip art images, different values for the rise and run are given, but in all cases they result in the same slope for the staircase. These images help advance the idea that slope is a ratio and proportion.

Math Clip Art: Types of Slope

Use these clip art images to show the different types of slope available. These slope types are covered:

Math Clip Art: Types of Slope

Use these clip art images to show the different types of slope available. These slope types are covered:

Topic

Slope Formula

Description

This example demonstrates how to calculate the slope of a line connecting two points on a coordinate grid. The points (1, 2) and (7, 6) are plotted, and the slope formula is applied to find the slope between them. The calculation shows that the slope is (6 - 2) / (7 - 1) = 4 / 6 = 2 / 3.

The slope formula is a fundamental concept in coordinate geometry, allowing us to determine the steepness and direction of a line. It's essential for understanding linear relationships and is widely used in various mathematical and real-world applications.

Topic

Slope Formula

Description

This example demonstrates how to calculate the slope of a line connecting two points on a coordinate grid. The points (1, 2) and (7, 6) are plotted, and the slope formula is applied to find the slope between them. The calculation shows that the slope is (6 - 2) / (7 - 1) = 4 / 6 = 2 / 3.

The slope formula is a fundamental concept in coordinate geometry, allowing us to determine the steepness and direction of a line. It's essential for understanding linear relationships and is widely used in various mathematical and real-world applications.

Topic

Slope Formula

Description

This example demonstrates how to calculate the slope of a line connecting two points on a coordinate grid. The points (1, 2) and (7, 6) are plotted, and the slope formula is applied to find the slope between them. The calculation shows that the slope is (6 - 2) / (7 - 1) = 4 / 6 = 2 / 3.

The slope formula is a fundamental concept in coordinate geometry, allowing us to determine the steepness and direction of a line. It's essential for understanding linear relationships and is widely used in various mathematical and real-world applications.

Topic

Slope Formula

Description

This example illustrates the calculation of slope for a line connecting two points: (1, 6) and (10, -3) on a Cartesian plane. Applying the slope formula, we find that the slope is (6 - (-3)) / (1 - 10) = 9 / -9 = -1.

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 slope.

Topic

Slope Formula

Description

This example illustrates the calculation of slope for a line connecting two points: (1, 6) and (10, -3) on a Cartesian plane. Applying the slope formula, we find that the slope is (6 - (-3)) / (1 - 10) = 9 / -9 = -1.

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 slope.

Topic

Slope Formula

Description

This example illustrates the calculation of slope for a line connecting two points: (1, 6) and (10, -3) on a Cartesian plane. Applying the slope formula, we find that the slope is (6 - (-3)) / (1 - 10) = 9 / -9 = -1.

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 slope.

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a vertical line connecting points (5, 6) and (5, -8) on a Cartesian plane. When we apply the slope formula, we find that the slope is (6 - (-8)) / (5 - 5) = 14 / 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.

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a vertical line connecting points (5, 6) and (5, -8) on a Cartesian plane. When we apply the slope formula, we find that the slope is (6 - (-8)) / (5 - 5) = 14 / 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.

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a vertical line connecting points (5, 6) and (5, -8) on a Cartesian plane. When we apply the slope formula, we find that the slope is (6 - (-8)) / (5 - 5) = 14 / 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.

Topic

Slope Formula

Description

This example illustrates the calculation of slope for a line connecting two points: (-2, 6) and (-4, -8) on a Cartesian plane. Applying the slope formula, we find that the slope is (6 - (-8)) / (-2 - (-4)) = 14 / 2 = 7.

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 with negative coordinates when calculating slope, resulting in a positive slope.

Topic

Slope Formula

Description

This example illustrates the calculation of slope for a line connecting two points: (-2, 6) and (-4, -8) on a Cartesian plane. Applying the slope formula, we find that the slope is (6 - (-8)) / (-2 - (-4)) = 14 / 2 = 7.

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 with negative coordinates when calculating slope, resulting in a positive slope.

Topic

Slope Formula

Description

This example illustrates the calculation of slope for a line connecting two points: (-2, 6) and (-4, -8) on a Cartesian plane. Applying the slope formula, we find that the slope is (6 - (-8)) / (-2 - (-4)) = 14 / 2 = 7.

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 with negative coordinates when calculating slope, resulting in a positive slope.

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a line connecting two points: (-10, 6) and (-1, -1) on a Cartesian plane. The line crosses quadrants II and III. Applying the slope formula, we find that the slope is (6 - (-1)) / (-10 - (-1)) = 7 / -9 = -7 / 9.

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 points in different quadrants and with negative coordinates when calculating slope.

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a line connecting two points: (-10, 6) and (-1, -1) on a Cartesian plane. The line crosses quadrants II and III. Applying the slope formula, we find that the slope is (6 - (-1)) / (-10 - (-1)) = 7 / -9 = -7 / 9.

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 points in different quadrants and with negative coordinates when calculating slope.

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a line connecting two points: (-10, 6) and (-1, -1) on a Cartesian plane. The line crosses quadrants II and III. Applying the slope formula, we find that the slope is (6 - (-1)) / (-10 - (-1)) = 7 / -9 = -7 / 9.

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 points in different quadrants and with negative coordinates when calculating slope.

Topic

Slope Formula

Description

This example illustrates the calculation of slope for a vertical line passing through two points: (-5, 6) and (-5, -4) in Quadrant II of a Cartesian plane. When we apply the slope formula, we find that the slope is (6 - (-4)) / (-5 - (-5)) = 10 / 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.

Topic

Slope Formula

Description

This example illustrates the calculation of slope for a vertical line passing through two points: (-5, 6) and (-5, -4) in Quadrant II of a Cartesian plane. When we apply the slope formula, we find that the slope is (6 - (-4)) / (-5 - (-5)) = 10 / 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.

Topic

Slope Formula

Description

This example illustrates the calculation of slope for a vertical line passing through two points: (-5, 6) and (-5, -4) in Quadrant II of a Cartesian plane. When we apply the slope formula, we find that the slope is (6 - (-4)) / (-5 - (-5)) = 10 / 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.

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a line connecting two points: (4, -5) and (-2, -7) on a Cartesian plane. The line crosses quadrants III and IV. Applying the slope formula, we find that the slope is (-5 - (-7)) / (4 - (-2)) = 2 / 6 = 1 / 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 negative coordinates and in different quadrants when calculating slope.

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a line connecting two points: (4, -5) and (-2, -7) on a Cartesian plane. The line crosses quadrants III and IV. Applying the slope formula, we find that the slope is (-5 - (-7)) / (4 - (-2)) = 2 / 6 = 1 / 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 negative coordinates and in different quadrants when calculating slope.

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a line connecting two points: (4, -5) and (-2, -7) on a Cartesian plane. The line crosses quadrants III and IV. Applying the slope formula, we find that the slope is (-5 - (-7)) / (4 - (-2)) = 2 / 6 = 1 / 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 negative coordinates and in different quadrants when calculating slope.

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a line connecting two points: (9, -10) and (-1, -2) on a Cartesian plane. The line crosses quadrants III and IV diagonally. Applying the slope formula, we find that the slope is (-2 - (-10)) / (-1 - 9) = 8 / -10 = -4 / 5.

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 negative fraction.

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a line connecting two points: (9, -10) and (-1, -2) on a Cartesian plane. The line crosses quadrants III and IV diagonally. Applying the slope formula, we find that the slope is (-2 - (-10)) / (-1 - 9) = 8 / -10 = -4 / 5.

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 negative fraction.

Topic

Slope Formula

Description

This example demonstrates the calculation of slope for a line connecting two points: (9, -10) and (-1, -2) on a Cartesian plane. The line crosses quadrants III and IV diagonally. Applying the slope formula, we find that the slope is (-2 - (-10)) / (-1 - 9) = 8 / -10 = -4 / 5.

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 negative fraction.

Topic

Slope Formula

Description

This 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.

Topic

Slope Formula

Description

This 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.

Topic

Slope Formula

Description

This 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.

Topic

Slope Formula

Description

This 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.

Topic

Slope Formula

Description

This 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.

Topic

Slope Formula

Description

This 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.

Topic

Slope Formula

Description

This 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.

Topic

Slope Formula

Description

This 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.

Topic

Slope Formula

Description

This 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.

Topic

Slope Formula

Description

This 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.

Topic

Slope Formula

Description

This 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.

Topic

Slope Formula

Description

This 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.

Topic

Slope Formula

Description

This 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.

Topic

Slope Formula

Description

This 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.

Topic

Slope Formula

Description

This 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.

Topic

Slope Formula

Description

This 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.

Topic

Slope Formula

Description

This 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.

Topic

Slope Formula

Description

This 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.

Topic

Slope Formula

Description

This 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.

Topic

Slope Formula

Description

This 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.