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Illustrative Math-Media4Math Alignment

 

 

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
Math Example--Coordinate Geometry--Slope Formula: Example 4 Math Example--Coordinate Geometry--Slope Formula: Example 4 Math Example--Coordinate Geometry--Slope Formula: Example 4

This is part of a collection of math examples that focus on coordinate geometry. This includes using coordinates to find the slope, midpoint, and distance.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 4 Math Example--Coordinate Geometry--Slope Formula: Example 4 Math Example--Coordinate Geometry--Slope Formula: Example 4

This is part of a collection of math examples that focus on coordinate geometry. This includes using coordinates to find the slope, midpoint, and distance.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 5 Math Example--Coordinate Geometry--Slope Formula: Example 5 Math Example--Coordinate Geometry--Slope Formula: Example 5

This is part of a collection of math examples that focus on coordinate geometry. This includes using coordinates to find the slope, midpoint, and distance.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 5 Math Example--Coordinate Geometry--Slope Formula: Example 5 Math Example--Coordinate Geometry--Slope Formula: Example 5

This is part of a collection of math examples that focus on coordinate geometry. This includes using coordinates to find the slope, midpoint, and distance.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 5 Math Example--Coordinate Geometry--Slope Formula: Example 5 Math Example--Coordinate Geometry--Slope Formula: Example 5

This is part of a collection of math examples that focus on coordinate geometry. This includes using coordinates to find the slope, midpoint, and distance.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 6 Math Example--Coordinate Geometry--Slope Formula: Example 6 Math Example--Coordinate Geometry--Slope Formula: Example 6

This is part of a collection of math examples that focus on coordinate geometry. This includes using coordinates to find the slope, midpoint, and distance.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 6 Math Example--Coordinate Geometry--Slope Formula: Example 6 Math Example--Coordinate Geometry--Slope Formula: Example 6

This is part of a collection of math examples that focus on coordinate geometry. This includes using coordinates to find the slope, midpoint, and distance.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 6 Math Example--Coordinate Geometry--Slope Formula: Example 6 Math Example--Coordinate Geometry--Slope Formula: Example 6

This is part of a collection of math examples that focus on coordinate geometry. This includes using coordinates to find the slope, midpoint, and distance.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 7 Math Example--Coordinate Geometry--Slope Formula: Example 7 Math Example--Coordinate Geometry--Slope Formula: Example 7

This is part of a collection of math examples that focus on coordinate geometry. This includes using coordinates to find the slope, midpoint, and distance.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 7 Math Example--Coordinate Geometry--Slope Formula: Example 7 Math Example--Coordinate Geometry--Slope Formula: Example 7

This is part of a collection of math examples that focus on coordinate geometry. This includes using coordinates to find the slope, midpoint, and distance.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 7 Math Example--Coordinate Geometry--Slope Formula: Example 7 Math Example--Coordinate Geometry--Slope Formula: Example 7

This is part of a collection of math examples that focus on coordinate geometry. This includes using coordinates to find the slope, midpoint, and distance.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 8 Math Example--Coordinate Geometry--Slope Formula: Example 8 Math Example--Coordinate Geometry--Slope Formula: Example 8

This is part of a collection of math examples that focus on coordinate geometry. This includes using coordinates to find the slope, midpoint, and distance.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 8 Math Example--Coordinate Geometry--Slope Formula: Example 8 Math Example--Coordinate Geometry--Slope Formula: Example 8

This is part of a collection of math examples that focus on coordinate geometry. This includes using coordinates to find the slope, midpoint, and distance.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 8 Math Example--Coordinate Geometry--Slope Formula: Example 8 Math Example--Coordinate Geometry--Slope Formula: Example 8

This is part of a collection of math examples that focus on coordinate geometry. This includes using coordinates to find the slope, midpoint, and distance.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 9 Math Example--Coordinate Geometry--Slope Formula: Example 9 Math Example--Coordinate Geometry--Slope Formula: Example 9

This is part of a collection of math examples that focus on coordinate geometry. This includes using coordinates to find the slope, midpoint, and distance.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 9 Math Example--Coordinate Geometry--Slope Formula: Example 9 Math Example--Coordinate Geometry--Slope Formula: Example 9

This is part of a collection of math examples that focus on coordinate geometry. This includes using coordinates to find the slope, midpoint, and distance.

Slope
Math Example--Coordinate Geometry--Slope Formula: Example 9 Math Example--Coordinate Geometry--Slope Formula: Example 9 Math Example--Coordinate Geometry--Slope Formula: Example 9

This is part of a collection of math examples that focus on coordinate geometry. This includes using coordinates to find the slope, midpoint, and distance.

Slope
Math Example--Linear Function Concepts--Evaluating Linear Functions: Example 1 Math Example--Linear Function Concepts--Evaluating Linear Functions: Example 1 Math Example--Linear Function Concepts--Evaluating Linear Functions: Example 1

This is part of a collection of math examples that focus on linear function concepts.

Slope-Intercept Form
Math Example--Linear Function Concepts--Evaluating Linear Functions: Example 10 Math Example--Linear Function Concepts--Evaluating Linear Functions: Example 10 Math Example--Linear Function Concepts--Evaluating Linear Functions: Example 10

This is part of a collection of math examples that focus on linear function concepts.

Slope-Intercept Form
Math Example--Linear Function Concepts--Evaluating Linear Functions: Example 2 Math Example--Linear Function Concepts--Evaluating Linear Functions: Example 2 Math Example--Linear Function Concepts--Evaluating Linear Functions: Example 2

This is part of a collection of math examples that focus on linear function concepts.

Slope-Intercept Form
Math Example--Linear Function Concepts--Evaluating Linear Functions: Example 3 Math Example--Linear Function Concepts--Evaluating Linear Functions: Example 3 Math Example--Linear Function Concepts--Evaluating Linear Functions: Example 3

This is part of a collection of math examples that focus on linear function concepts.

Slope-Intercept Form
Math Example--Linear Function Concepts--Evaluating Linear Functions: Example 4 Math Example--Linear Function Concepts--Evaluating Linear Functions: Example 4 Math Example--Linear Function Concepts--Evaluating Linear Functions: Example 4

This is part of a collection of math examples that focus on linear function concepts.

Slope-Intercept Form
Math Example--Linear Function Concepts--Evaluating Linear Functions: Example 5 Math Example--Linear Function Concepts--Evaluating Linear Functions: Example 5 Math Example--Linear Function Concepts--Evaluating Linear Functions: Example 5

This is part of a collection of math examples that focus on linear function concepts.

Slope-Intercept Form
Math Example--Linear Function Concepts--Evaluating Linear Functions: Example 6 Math Example--Linear Function Concepts--Evaluating Linear Functions: Example 6 Math Example--Linear Function Concepts--Evaluating Linear Functions: Example 6

This is part of a collection of math examples that focus on linear function concepts.

Slope-Intercept Form
Math Example--Linear Function Concepts--Evaluating Linear Functions: Example 7 Math Example--Linear Function Concepts--Evaluating Linear Functions: Example 7 Math Example--Linear Function Concepts--Evaluating Linear Functions: Example 7

This is part of a collection of math examples that focus on linear function concepts.

Slope-Intercept Form
Math Example--Linear Function Concepts--Evaluating Linear Functions: Example 8 Math Example--Linear Function Concepts--Evaluating Linear Functions: Example 8 Math Example--Linear Function Concepts--Evaluating Linear Functions: Example 8

This is part of a collection of math examples that focus on linear function concepts.

Slope-Intercept Form
Math Example--Linear Function Concepts--Evaluating Linear Functions: Example 9 Math Example--Linear Function Concepts--Evaluating Linear Functions: Example 9 Math Example--Linear Function Concepts--Evaluating Linear Functions: Example 9

This is part of a collection of math examples that focus on linear function concepts.

Slope-Intercept Form
Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 1 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 1 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 1

Topic

Linear Functions

Description

This example demonstrates how to graph a linear function with a slope of 2 and a y-intercept of 3. The process involves three key steps: first, plotting the y-intercept at (0, 3); second, using the slope to find another point on the line; and finally, connecting these points to form the line.

Slope-Intercept Form
Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 10 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 10 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 10

Topic

Linear Functions

Description

This example illustrates the process of graphing a linear function with a slope of -4 and a y-intercept of 0. The method involves three main steps: plotting the y-intercept at the origin (0, 0), using the slope to determine a second point on the line, and connecting these points to create the linear graph.

Slope-Intercept Form
Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 11 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 11 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 11

Topic

Linear Functions

Description

This example demonstrates the process of graphing a linear function with a slope of 0 and a y-intercept of 5. The procedure involves three key steps: plotting the y-intercept at (0, 5), recognizing that a slope of 0 results in a horizontal line, and drawing the line parallel to the x-axis through the y-intercept.

Slope-Intercept Form
Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 12 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 12 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 12

Topic

Linear Functions

Description

This example illustrates the process of graphing a linear function with a slope of 0 and a y-intercept of -5. The method involves three main steps: plotting the y-intercept at (0, -5), recognizing that a slope of 0 results in a horizontal line, and drawing the line parallel to the x-axis through the y-intercept.

Slope-Intercept Form
Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 13 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 13 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 13

Topic

Linear Functions

Description

This example demonstrates how to graph a linear function with a slope of 0 and a y-intercept of 0. The process involves recognizing that this special case results in a horizontal line coinciding with the x-axis. The line passes through the origin (0, 0) and extends infinitely in both directions along the x-axis.

Slope-Intercept Form
Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 2 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 2 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 2

Topic

Linear Functions

Description

This example illustrates the process of graphing a linear function with a slope of 0.5 and a y-intercept of 3. The method involves three main steps: plotting the y-intercept at (0, 3), using the slope to determine a second point on the line, and connecting these points to create the linear graph.

Slope-Intercept Form
Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 3 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 3 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 3

Topic

Linear Functions

Description

This example demonstrates the process of graphing a linear function with a slope of 5 and a y-intercept of -4. The procedure involves three key steps: plotting the y-intercept at (0, -4), using the slope to determine a second point on the line, and connecting these points to form the linear graph.

Slope-Intercept Form
Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 4 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 4 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 4

Topic

Linear Functions

Description

This example illustrates the process of graphing a linear function with a slope of 0.1 and a y-intercept of -4. The method involves three main steps: plotting the y-intercept at (0, -4), using the slope to determine a second point on the line, and connecting these points to create the linear graph.

Slope-Intercept Form
Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 5 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 5 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 5

Topic

Linear Functions

Description

This example demonstrates how to graph a linear function with a slope of -4 and a y-intercept of 5. The process involves three key steps: first, plotting the y-intercept at (0, 5); second, using the slope to find another point on the line; and finally, connecting these points to form the line.

Slope-Intercept Form
Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 6 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 6 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 6

Topic

Linear Functions

Description

This example illustrates the process of graphing a linear function with a slope of -1/3 and a y-intercept of 5. The method involves three main steps: plotting the y-intercept at (0, 5), using the slope to determine a second point on the line, and connecting these points to create the linear graph.

Slope-Intercept Form
Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 7 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 7 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 7

Topic

Linear Functions

Description

This example demonstrates the process of graphing a linear function with a slope of -3 and a y-intercept of -2. The procedure involves three key steps: plotting the y-intercept at (0, -2), using the slope to determine a second point on the line, and connecting these points to form the linear graph.

Slope-Intercept Form
Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 8 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 8 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 8

Topic

Linear Functions

Description

This example illustrates the process of graphing a linear function with a slope of -0.25 and a y-intercept of -2. The method involves three main steps: plotting the y-intercept at (0, -2), using the slope to determine a second point on the line, and connecting these points to create the linear graph.

Slope-Intercept Form
Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 9 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 9 Math Example--Linear Function Concepts--Graphs of Linear Functions in Slope-Intercept Form: Example 9

Topic

Linear Functions

Description

This example demonstrates how to graph a linear function with a slope of 0.25 and a y-intercept of 0. The process involves three key steps: first, plotting the y-intercept at the origin (0, 0); second, using the slope to find another point on the line; and finally, connecting these points to form the line.

Slope-Intercept Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1

Topic

Linear Functions

Description

This example demonstrates the process of converting a linear equation from standard form to slope-intercept form. The equation 2x + 4y = 8 is solved step-by-step, isolating y and dividing by its coefficient. The result is y = -1/2 x + 2, clearly showing the slope and y-intercept of the line.

Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1

Topic

Linear Functions

Description

This example demonstrates the process of converting a linear equation from standard form to slope-intercept form. The equation 2x + 4y = 8 is solved step-by-step, isolating y and dividing by its coefficient. The result is y = -1/2 x + 2, clearly showing the slope and y-intercept of the line.

Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1

Topic

Linear Functions

Description

This example demonstrates the process of converting a linear equation from standard form to slope-intercept form. The equation 2x + 4y = 8 is solved step-by-step, isolating y and dividing by its coefficient. The result is y = -1/2 x + 2, clearly showing the slope and y-intercept of the line.

Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1

Topic

Linear Functions

Description

This example demonstrates the process of converting a linear equation from standard form to slope-intercept form. The equation 2x + 4y = 8 is solved step-by-step, isolating y and dividing by its coefficient. The result is y = -1/2 x + 2, clearly showing the slope and y-intercept of the line.

Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1

Topic

Linear Functions

Description

This example demonstrates the process of converting a linear equation from standard form to slope-intercept form. The equation 2x + 4y = 8 is solved step-by-step, isolating y and dividing by its coefficient. The result is y = -1/2 x + 2, clearly showing the slope and y-intercept of the line.

Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1

Topic

Linear Functions

Description

This example demonstrates the process of converting a linear equation from standard form to slope-intercept form. The equation 2x + 4y = 8 is solved step-by-step, isolating y and dividing by its coefficient. The result is y = -1/2 x + 2, clearly showing the slope and y-intercept of the line.

Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1

Topic

Linear Functions

Description

This example demonstrates the process of converting a linear equation from standard form to slope-intercept form. The equation 2x + 4y = 8 is solved step-by-step, isolating y and dividing by its coefficient. The result is y = -1/2 x + 2, clearly showing the slope and y-intercept of the line.

Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1

Topic

Linear Functions

Description

This example demonstrates the process of converting a linear equation from standard form to slope-intercept form. The equation 2x + 4y = 8 is solved step-by-step, isolating y and dividing by its coefficient. The result is y = -1/2 x + 2, clearly showing the slope and y-intercept of the line.

Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1

Topic

Linear Functions

Description

This example demonstrates the process of converting a linear equation from standard form to slope-intercept form. The equation 2x + 4y = 8 is solved step-by-step, isolating y and dividing by its coefficient. The result is y = -1/2 x + 2, clearly showing the slope and y-intercept of the line.

Standard Form
Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 10 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 10 Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 10

Topic

Linear Functions

Description

This example illustrates the conversion of the linear equation x + y = 1 from standard form to slope-intercept form. The process involves isolating y, resulting in y = -x + 1. This simple transformation clearly reveals the slope and y-intercept of the line.

Standard Form