Illustrative Math Alignment: Grade 8 Unit 3

This is part of a collection of math quizzes on the topic of solving proportions. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

This is part of a collection of math quizzes on the topic of solving proportions. Some quizzes are interactive and some are in PDF format.

Related Resources

Quiz Library

Topic

Linear Functions

Description

This image is the first in a series of 6 clip art images that show step by step how to use the slope formula. It serves as an introduction, with the title "Introduction" and includes the text "In this presentation, we walk you through the steps of using the Slope Formula." The image features a linear graph with two generic points highlighted and the slope formula displayed.

Topic

Linear Functions

Description

This image is the first in a series of 6 clip art images that show step by step how to use the slope formula. It serves as an introduction, with the title "Introduction" and includes the text "In this presentation, we walk you through the steps of using the Slope Formula." The image features a linear graph with two generic points highlighted and the slope formula displayed.

Topic

Linear Functions

Description

This image is a continuation of the previous one, focusing on Step 1 of using the slope formula: "Identify the Coordinates." The example in this series of images deals with coordinates (3, 4) and (-5, -4), demonstrating how to select two points on a line to calculate its slope.

Teachers can guide students through this step by saying: "The first step in using the slope formula is to identify two points on our line. In this example, we're using the points (3, 4) and (-5, -4). Can you locate these points on the graph? Why do you think it's important to choose two different points?"

Topic

Linear Functions

Description

This image is a continuation of the previous one, focusing on Step 1 of using the slope formula: "Identify the Coordinates." The example in this series of images deals with coordinates (3, 4) and (-5, -4), demonstrating how to select two points on a line to calculate its slope.

Teachers can guide students through this step by saying: "The first step in using the slope formula is to identify two points on our line. In this example, we're using the points (3, 4) and (-5, -4). Can you locate these points on the graph? Why do you think it's important to choose two different points?"

Topic

Linear Functions

Description

This image continues the series, focusing on Step 2 of using the slope formula: "Match Coordinates to Formula." It demonstrates how to correctly assign the chosen coordinates to the variables in the slope formula.

Topic

Linear Functions

Description

This image continues the series, focusing on Step 2 of using the slope formula: "Match Coordinates to Formula." It demonstrates how to correctly assign the chosen coordinates to the variables in the slope formula.

Topic

Linear Functions

Description

This image focuses on Step 3 of using the slope formula: "Assign Values to Formula." It shows how to substitute the actual coordinate values into the slope formula, preparing for the calculation of the slope.

Topic

Linear Functions

Description

This image focuses on Step 3 of using the slope formula: "Assign Values to Formula." It shows how to substitute the actual coordinate values into the slope formula, preparing for the calculation of the slope.

Topic

Linear Functions

Description

This image continues the series, focusing on Step 4 of using the slope formula: "Assign Values to Formula." It completes the assignment of coordinate values in the slope formula. In this case we deal with x2 and y2.

Teachers can walk students through this step by saying: "Now we complete the assignment of coordinate values into the slope formula. In this case we deal with x2 and y2. Do you see how those coordinates are highlighted in the formula?"

Topic

Linear Functions

Description

This image continues the series, focusing on Step 4 of using the slope formula: "Assign Values to Formula." It completes the assignment of coordinate values in the slope formula. In this case we deal with x2 and y2.

Teachers can walk students through this step by saying: "Now we complete the assignment of coordinate values into the slope formula. In this case we deal with x2 and y2. Do you see how those coordinates are highlighted in the formula?"

Topic

Linear Functions

Description

This final image in the series focuses on Step 5 of using the slope formula: "Simplify." It shows how to express the calculated slope in its simplest form, if necessary.

Teachers can conclude the lesson with this step by saying: "Our last step is to simplify our result if possible. Sometimes, our slope might be a fraction that can be reduced. Other times, it might already be in its simplest form. Why is it important to express our slope in the simplest possible way? How does this final step help us interpret what the slope means in the context of our line?"

Topic

Linear Functions

Description

This final image in the series focuses on Step 5 of using the slope formula: "Simplify." It shows how to express the calculated slope in its simplest form, if necessary.

Teachers can conclude the lesson with this step by saying: "Our last step is to simplify our result if possible. Sometimes, our slope might be a fraction that can be reduced. Other times, it might already be in its simplest form. Why is it important to express our slope in the simplest possible way? How does this final step help us interpret what the slope means in the context of our line?"

Use this selection of images to show steepness of stairs as a way of introducing the concept of slope.

Use this selection of images to show steepness of stairs as a way of introducing the concept of slope.

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.

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.

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.