Question

A movie theater offers a reward program that charges a yearly membership fee and a discounted rate per movie ticket. The total cost for a reward program member to see 5 movies is $40 and the total cost for 12 movies is $75. Assume the relationship is linear. Write the equation of the function in the form y=mx+b , where x represents the number of movies and y represents the total cost.

Hint: Treat this information like ordered pairs. (5, 40) and (12, 75)

Answer 1

`y=5x+15`

Explanation:

Since this situation is a linear relationship between the number of movies and the total cost, we need to determine the slope of the line given our two ordered pairs
`(x_1,y_1)\rightarrow(5,40)` and
`(x_2,y_2)\rightarrow(12,75)`:

`m=(y_2-y_1)/(x_2-x_1)\\ \\m=(75-40)/(12-5)\\ \\m=(35)/(7)\\ \\m=5`

Thus, our equation so far is
`y=5x+b`. Next, we need to find our y-intercept,
`b`, which represents our flat fee. We do so by using one of our original given ordered pairs:

`y=5x+b\\\\40=5(5)+b\\\\40=25+b\\\\15=b`

Therefore, our final equation for the function is
`y=5x+15`