Write linear equations from tables or graphs.

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 -30 01 32 6

Linear Functions: A function whose graph is a line.

Y-intercept:Where the line crosses the y-axisb is the symbol for the y-intercept

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

Setting up the equation Find b

(0,??)y-intercept is where the line crosses the y-axis

Find slope y/xthe # are you counting by for the y valuesrise over run

Y = ?? ± slope times x

y = b ± mx

Find the linear equation for the input-output table.

Start Value ispaired with 0. Start value is 11.

y = 11 ± ____x

Find differencein the outputs.

Rate of change is the difference: – 3

Finish the equation. y = 11 – 3x

Find the linear equation forthe 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

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

2. Use the equation y = –5 + x.

a) What is the rate of change?

b) What is the start value?

c) Is the graph of this function a) increasing or b) decreasing?

How do you know?

Inputx

Outputy

-1 50 31 12 -13 -3

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

Writing Linear Equations

Lesson 25

1. Given a linear graph, create an input-output table using the ordered pairs of the points on the graph.

2. Determine the start value (the output number paired with an input of zero).

3. Determine the rate of change (the amount the output number increases or decreases when the x-value increases by one unit).

4. Write the equation by filling in the start value, operation and rate of change:

y = __ ± __ x