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>
Slope formula:
where
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
Since
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>