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.
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, (x_{1}, y_{1}) and (x_{2}, y_{2}), to find the slope.
Find the ratio between change in y-values and change in x-vales.
m = (y_{2} - y_{1})/(x_{2} - x_{1})
Substitute :
(x_{1}, y_{1}) = (0, 8)
(x_{2}, y_{2}) = (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, (x_{1}, y_{1}) and (x_{2}, y_{2}), to find the slope.
Find the ratio between change in y-values and change in x-values.
m = (y_{2} - y_{1})/(x_{2} - x_{1})
Substitute :
(x_{1}, y_{1}) = (0, 25)
(x_{2}, y_{2}) = (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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