# WRITING AN EQUATION FROM A GRAPH

## About "Writing an equation from a graph"

Writing an equation from a graph :

We can use information presented in a graph to write an equation in slope-intercept form.

## Writing an equation from a graph - Examples

Example 1 :

A video club charges a one-time membership fee plus a rental fee for each DVD borrowed. Use the graph to write an equation in slope-intercept form to represent the amount spent, y, on x DVD rentals. Solution :

Step 1 :

Choose two points on the graph, (x, y) and (x, y), to find the slope.

Find the ratio between change in y-values and change in x-

m  =  (y₂ - y) / (xx)

Substitute (0, 8) for (x, yand (8, 18) for (x, y).

m  =  (18 - 8) / (8 - 0)

m  =  10 / 8

m  =  1.25

Step 2 :

Read the y-intercept from the graph. That is, the point at which the line cuts y-axis.

The y-intercept is 8.

b  =  8

Step 3 :

Let us use slope (m) and y-intercept (b) values to write an equation in slope-intercept form.

y  =  mx + b (Slope-intercept form)

Plug m  =  1.25 and b  =  8.

y  =  1.25x + 8

Example 2 :

The cash register subtracts \$2.50 from a \$25 Coffee Café gift card for every medium coffee the customer buys. Use the graph to write an equation in slope-intercept form to represent this situation. Solution :

Step 1 :

Choose two points on the graph, (x, y) and (x, y), to find the slope.

Find the ratio between change in y-values and change in x-

m  =  (y₂ - y) / (x - x)

Substitute (0, 25) for (x, yand (10, 0) for (x, y).

m  =  (0 - 25) / (10 - 0)

m  =  -25 / 10

m  =  -2.5

Step 2 :

Read the y-intercept from the graph. That is, the point at which the line cuts y-axis.

The y-intercept is 25.

Step 3 :

Let us use slope (m) and y-intercept (b) values to write an equation in slope-intercept form.

y  =  -2.5x + 25 (Slope-intercept form)

Plug m  =  -2.5 and b  =  25.

y  =  -2.5x + 25 After having gone through the stuff given above, we hope that the students would have understood "Writing an equation from a graph".