WRITING AN EQUATION FROM A GRAPH WORKSHEET

Problem 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.

Problem 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.

Answers

Problem 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

Problem 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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