To solve this, we are going to use the slope formula, and the point slope formula.
Slope formula:

where

is the slope.

are the coordinates of the first point.

are the coordinates of the first point.
Point-slope formula:
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:



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




Remember that in a linear equation of the form

,

is the slope and

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

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).







Membership fee:
$8
Plan C. Coordinates of the first point: (1,10). Coordinates of the second point: (2,15).







Membership fee:
$5
Part D. Coordinates of the first point: (1,12). Coordinates of the second point (2,21).







Membership fee:
$3
We can conclude that the plan that has the smallest one-time membership is <span>
Plan D.</span>