# Linear Relationships

## Objective

Write equations into slope-intercept form in order to graph. Graph vertical and horizontal lines.

## Common Core Standards

### Core Standards

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• 8.EE.B.6 — Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

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• 8.EE.C.7

## Criteria for Success

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1. Distinguish between standard form and slope-intercept form.
2. Rewrite an equation into slope-intercept form by solving for $y$.
3. Graph a linear equation using the slope and $y$-intercept.
4. Understand that the equation $y=a$, where a is a constant, is a horizontal line with a zero slope, and the equation ${x=a}$ is a vertical line with undefined slope.

## Tips for Teachers

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Lesson 9 is a continuation of Lesson 8 but presents equations in standard form that are then written into slope-intercept form as a strategy to graph.

### Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problems 2 and 3 (benefit from worked examples). Find more guidance on adapting our math curriculum for remote learning here.

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## Anchor Problems

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### Problem 1

Given the equation ${2x+3y=9}$, determine the slope and $y$-intercept, and then graph the line that represents the equation. #### Guiding Questions

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### Problem 2

Write the equation below into slope-intercept form and then graph the line that represents the equation.

${-4x-2y=-5}$ #### Guiding Questions

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### Problem 3

Match each equation to a graph. Be prepared to explain your reasoning.

Equation A: ${ y=5}$
Equation B: ${x=5}$  #### Guiding Questions

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## Problem Set

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## Target Task

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Identify the slope and $y$-intercept of the equation $12x-8y=24$.
Then graph the line that represents the equation. Create a free account or sign in to view Mastery Response