Question

A movie streaming service charges a set fee for
membership each month, plus an additional fee
for the number of movies streamed each
month. If 2 movies are streamed, the cost is
$14 per month, however if 6 movies are
streamed, the cost is $20. Write an equation to
model the cost, y, based on the number of
movies streamed x.

Answer 1

We can start by setting up a system of two equations, one for each scenario:

When 2 movies are streamed:
y = a + bx
14 = a + 2b

When 6 movies are streamed:
y = a + bx
20 = a + 6b

Now we can solve for a and b by using either substitution or elimination. Let's use elimination:

Multiplying the first equation by -3:
-42 = -3a - 6b

Multiplying the second equation by 2:
40 = 2a + 12b

Adding the two equations:
-2 = -a + 6b

Solving for a:
a = 6b + 2

Now we can substitute this expression for a into one of the original equations (let's use the first one):

14 = (6b + 2) + 2b

Solving for b:
12 = 8b
b = 1.5

Finally, we can substitute both values of a and b into the equation for y:

y = (6b + 2) + bx
y = 6(1.5) + 2x
y = 9 + 2x

Therefore, the equation to model the cost based on the number of movies streamed is:
y = 9 + 2x