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**Write linear equations from tables or graphs.**

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**Use the table below to answer the following questions.**

Does the graph model direct variation? What is the slope? Write an equation for the graph. x y -2 -6 -1 -3 1 3 2 6

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Linear Functions: A function whose graph is a line. Y-intercept: Where the line crosses the y-axis b is the symbol for the y-intercept

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**Look for a pattern What # are you counting by for the y-values?**

What is y when x = 0 ? This is b … where the line crosses the y-axis … y-intercept y = b plus or minus the slope times x y = b ± mx

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**Setting up the equation**

Find b (0,??) y-intercept is where the line crosses the y-axis Find slope y/x the # are you counting by for the y values rise over run Y = ?? ± slope times x y = b ± mx

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**Example 1 Find the linear equation for the input-output table.**

Start Value is paired with 0. Start value is 11. y = 11 ± ____x Find difference in the outputs. Rate of change is the difference: – 3 Finish the equation y = 11 – 3x

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**Example 2 Find the linear equation for the graph.**

Create an input-output table from each point. Find start value: – 4 y = – 4 ± ____x Find rate of change: +2 Finish the equation. y = – 4 + 2x

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**Exit Problems Find the linear equation for the input-output table.**

y -1 5 3 1 2 -3 Find the linear equation for the input-output table. Use the equation y = –5 + x. What is the rate of change? What is the start value? Is the graph of this function a) increasing or b) decreasing? How do you know?

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Communication Prompt How is a direct variation equation a special type of linear equation?

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**Writing Linear Equations**

Lesson 25 Proportionality Writing Linear Equations

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**Writing Linear Equations from Tables and Graphs**

Given a linear graph, create an input-output table using the ordered pairs of the points on the graph. Determine the start value (the output number paired with an input of zero). Determine the rate of change (the amount the output number increases or decreases when the x-value increases by one unit). Write the equation by filling in the start value, operation and rate of change: y = __ ± __ x

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