WRITING AN EQUATION FROM A GRAPH

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, (x₁, y₁) and (x₂, y₂), to find the slope.

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

m  =  (y₂ - y₁) / (x₂ - x₁)

Substitute : 

(x₁, y₁)  =  (0, 8)

(x₂, y₂)  =  (8, 18)

Then, 

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)

Substitute 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, (x₁, y₁) and (x₂, y₂), to find the slope.

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

m  =  (y₂ - y₁) / (x₂ - x₁)

Substitute : 

(x₁, y₁)  =  (0, 25)

(x₂, y₂)  =  (10, 0)

Then, 

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)

Substitute m  =  -2.5 and b  =  25. 

y  =  -2.5x + 25

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