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

Answer:

$y=5x+15$

Step-by-step 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 $(x_2,y_2)\rightarrow(12,75)$:

$m=\frac{y_2-y_1}{x_2-x_1}\\ \\m=\frac{75-40}{12-5}\\ \\m=\frac{35}{7}\\ \\m=5$

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 $y=5x+15$