Illustrative Math Alignment: Grade 8 Unit 3
Linear Relationships
Lesson 9: Slopes Don't Have to be Positive
Use the following Media4Math resources with this Illustrative Math lesson.
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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 |
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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 |
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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 |
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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 |
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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
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 |
|
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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 |
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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 1TopicLinear Functions DescriptionThis 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 |
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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 10TopicLinear Functions DescriptionThis 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 |
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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 11TopicLinear Functions DescriptionThis 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 |
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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 12TopicLinear Functions DescriptionThis 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 |
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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 13TopicLinear Functions DescriptionThis 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 |
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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 2TopicLinear Functions DescriptionThis 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 |
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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 3TopicLinear Functions DescriptionThis 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 |
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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 4TopicLinear Functions DescriptionThis 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 |
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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 5TopicLinear Functions DescriptionThis 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 |
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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 6TopicLinear Functions DescriptionThis 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 |
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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 7TopicLinear Functions DescriptionThis 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 |
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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 8TopicLinear Functions DescriptionThis 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 |
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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 9TopicLinear Functions DescriptionThis 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 |
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Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1 | Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 1TopicLinear Functions DescriptionThis 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 |
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Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 10 | Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 10TopicLinear Functions DescriptionThis 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 |
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Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 11 | Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 11TopicLinear Functions DescriptionThis example showcases the transformation 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 step-by-step solution clearly reveals the slope and y-intercept of the line. |
Standard Form |
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Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 12 | Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 12TopicLinear Functions DescriptionThis example demonstrates the conversion of the linear equation x - y = 1 from standard form to slope-intercept form. The solution process involves isolating y and changing the sign of both sides, resulting in y = x - 1. This transformation clearly reveals the slope and y-intercept of the line. |
Standard Form |
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Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 13 | Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 13TopicLinear Functions DescriptionThis example illustrates the process of converting the linear equation -x + y = 1 from standard form to slope-intercept form. The solution involves rearranging the equation to isolate y, resulting in y = x + 1. This transformation clearly reveals the slope and y-intercept of the line. |
Standard Form |
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Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 14 | Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 14TopicLinear Functions DescriptionThis example demonstrates the conversion of the linear equation -x - y = -1 from standard form to slope-intercept form. The process involves manipulating the equation to solve for y, yielding y = -x + 1. This transformation clearly reveals the slope and y-intercept of the line. |
Standard Form |
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Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 15 | Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 15TopicLinear Functions DescriptionThis example showcases the transformation of the linear equation -x - y = 1 from standard form to slope-intercept form. The solution process involves isolating y, resulting in y = -x - 1. This step-by-step conversion clearly reveals the slope and y-intercept of the line. |
Standard Form |
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Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 16 | Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 16TopicLinear Functions DescriptionThis example demonstrates 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 transformation clearly reveals the slope and y-intercept of the line. Linear functions are fundamental mathematical concepts that describe relationships between two variables. The examples in this collection, such as showing step-by-step transformations from standard form to slope-intercept form, help in understanding how each part of the equation affects the graph and the relationship itself. |
Standard Form |
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Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 17 | Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 17TopicLinear Functions DescriptionThis example illustrates the conversion of the linear equation x - y = -1 from standard form to slope-intercept form. The solution involves isolating y, resulting in y = x + 1. This process clearly reveals the slope and y-intercept of the line. |
Standard Form |
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Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 18 | Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 18TopicLinear Functions DescriptionThis example demonstrates the conversion of the linear equation -x - y = 1 from standard form to slope-intercept form. The process involves rearranging the equation to isolate y, resulting in y = -x - 1. This transformation clearly reveals the slope and y-intercept of the line. |
Standard Form |
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Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 19 | Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 19TopicLinear Functions DescriptionThis example illustrates the conversion of the linear equation 12x + 28y = 0 from standard form to slope-intercept form. The solution involves isolating y and dividing by its coefficient, resulting in y = -3/7 x. This process clearly reveals the slope and y-intercept of the line. |
Standard Form |
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Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 2 | Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 2TopicLinear Functions DescriptionThis example illustrates the conversion of the linear equation 3x + 6y = -18 from standard form to slope-intercept form. The solution involves isolating y and dividing by its coefficient, resulting in y = -1/2 x - 3. This process clearly reveals the slope and y-intercept of the line. |
Standard Form |
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Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 20 | Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 20TopicLinear Functions DescriptionThis example demonstrates the conversion of the linear equation -14x - 35y = 0 from standard form to slope-intercept form. The process involves isolating y and dividing by its coefficient, resulting in y = -2/5 x. This transformation clearly reveals the slope and y-intercept of the line. |
Standard Form |
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Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 21 | Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 21TopicLinear Functions DescriptionThis example showcases the transformation of the linear equation 28x - 21y = 0 from standard form to slope-intercept form. The process involves isolating y and dividing by its coefficient, resulting in y = 4/3 x. This step-by-step solution clearly reveals the slope and y-intercept of the line. |
Standard Form |
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Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 22 | Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 22TopicLinear Functions DescriptionThis example illustrates the conversion of the linear equation -13x + 39y = 0 from standard form to slope-intercept form. The solution involves isolating y and dividing by its coefficient, resulting in y = 1/3 x. This process clearly reveals the slope and y-intercept of the line. |
Standard Form |
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Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 3 | Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 3TopicLinear Functions DescriptionThis example showcases the transformation of the linear equation 5x - 2y = 12 from standard form to slope-intercept form. The process involves isolating y and dividing by its coefficient, resulting in y = 2.5x - 6. This step-by-step solution clearly reveals the slope and y-intercept of the line. |
Standard Form |
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Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 4 | Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 4TopicLinear Functions DescriptionThis example demonstrates the conversion of the linear equation -6x + 10y = 20 from standard form to slope-intercept form. The solution process involves isolating y and dividing by its coefficient, resulting in y = 0.6x + 2. This transformation clearly reveals the slope and y-intercept of the line. |
Standard Form |
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Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 5 | Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 5TopicLinear Functions DescriptionThis example illustrates the process of converting the linear equation -9x - 15y = -45 from standard form to slope-intercept form. The solution involves rearranging the equation to isolate y, resulting in y = 3/5 x + 3. This transformation clearly reveals the slope and y-intercept of the line. |
Standard Form |
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Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 6 | Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 6TopicLinear Functions DescriptionThis example demonstrates the conversion of the linear equation -8x - 12y = 25 from standard form to slope-intercept form. The process involves manipulating the equation to solve for y, yielding y = -2/3 x - 25/12. This transformation clearly reveals the slope and y-intercept of the line. |
Standard Form |
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Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 7 | Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 7TopicLinear Functions DescriptionThis example illustrates the transformation of the linear equation -2x + 16y = -36 from standard form to slope-intercept form. The solution process involves solving for y, resulting in y = 1/8 x - 9/4. This step-by-step conversion clearly reveals the slope and y-intercept of the line. |
Standard Form |
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Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 8 | Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 8TopicLinear Functions DescriptionThis example showcases the conversion of the linear equation -7x + 21y = 63 from standard form to slope-intercept form. The process involves rearranging the equation to isolate y, resulting in y = 1/3 x + 3. This transformation clearly reveals the slope and y-intercept of the line. |
Standard Form |
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Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 9 | Math Example--Linear Function Concepts--Linear Equations in Standard Form: Example 9TopicLinear Functions DescriptionThis example demonstrates the process of converting the linear equation 10x - 28y = 56 from standard form to slope-intercept form. The solution involves isolating y and dividing by its coefficient, resulting in y = (5/14)x - 2. This transformation clearly reveals the slope and y-intercept of the line. |
Standard Form |
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Math Example--Linear Function Concepts--Linear Intercepts: Example 1 | Math Example--Linear Function Concepts--Linear Intercepts: Example 1
This is part of a collection of math examples that focus on linear function concepts. |
Slope-Intercept Form and Standard Form |
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Math Example--Linear Function Concepts--Linear Intercepts: Example 10 | Math Example--Linear Function Concepts--Linear Intercepts: Example 10
This is part of a collection of math examples that focus on linear function concepts. |
Slope-Intercept Form and Standard Form |
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Math Example--Linear Function Concepts--Linear Intercepts: Example 2 | Math Example--Linear Function Concepts--Linear Intercepts: Example 2
This is part of a collection of math examples that focus on linear function concepts. |
Slope-Intercept Form and Standard Form |
|
Math Example--Linear Function Concepts--Linear Intercepts: Example 3 | Math Example--Linear Function Concepts--Linear Intercepts: Example 3
This is part of a collection of math examples that focus on linear function concepts. |
Slope-Intercept Form and Standard Form |
|
Math Example--Linear Function Concepts--Linear Intercepts: Example 4 | Math Example--Linear Function Concepts--Linear Intercepts: Example 4
This is part of a collection of math examples that focus on linear function concepts. |
Slope-Intercept Form and Standard Form |
|
Math Example--Linear Function Concepts--Linear Intercepts: Example 5 | Math Example--Linear Function Concepts--Linear Intercepts: Example 5
This is part of a collection of math examples that focus on linear function concepts. |
Slope-Intercept Form and Standard Form |
|
Math Example--Linear Function Concepts--Linear Intercepts: Example 6 | Math Example--Linear Function Concepts--Linear Intercepts: Example 6
This is part of a collection of math examples that focus on linear function concepts. |
Slope-Intercept Form and Standard Form |
|
Math Example--Linear Function Concepts--Linear Intercepts: Example 7 | Math Example--Linear Function Concepts--Linear Intercepts: Example 7
This is part of a collection of math examples that focus on linear function concepts. |
Slope-Intercept Form and Standard Form |
