A company offers four plans for customers who want to rent DVDs and video games. The cost of the plans can be modeled by a linear function that combines a one time membership fe…

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asked May 19, 2019 63.3k views

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Levand · Answer 1 · 2019-05-25T06:49:21+0000

To solve this, we are going to use the slope formula, and the point slope formula.
Slope formula:
m= (y_(2)-y_(1))/(x_(2)-x_(1))

where

is the slope.

(x_(1),y_(1))

are the coordinates of the first point.

(x_(2),y_(2))

are the coordinates of the first point.
Point-slope formula:
y-y_(1)=m(x-x_(1))

Plan A. Coordinates of the first point: (1,14) (number of discs, cost). Coordinates of the second point: (2,17). Lets replace those values in our slope formula:

m= (y_(2)-y_(1))/(x_(2)-x_(1))

Now that we have the slope, we can use the point slope formula:

y-y_(1)=m(x-x_(1))

Remember that in a linear equation of the form
y=mx+b

,

is the slope and

is the y-intercept. In our model the y-intercept is the membership fee.
Since
b=11

in our linear equation, we can conclude that the membership fee is $11

Plan B. Coordinates of the first point (1,12). Coordinates of the second point (2,16).

m= (y_(2)-y_(1))/(x_(2)-x_(1))