Illustrative Math Alignment: Grade 8 Unit 3
Linear Relationships
Lesson 7: Representations of Linear Relationships
Use the following Media4Math resources with this Illustrative Math lesson.
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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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 |
