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.

Explanation:

Step1: Define given points

We have two points: $(x_1, y_1)=(5, 40)$ and $(x_2, y_2)=(12, 75)$

Step2: Calculate slope $m$

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

Step3: Find $b$ using point $(5,40)$

Substitute $x=5$, $y=40$, $m=5$ into $y=mx+b$:
$40=5(5)+b$
$40=25+b$
$b=40-25=15$

Step4: Write linear equation

Substitute $m=5$ and $b=15$ into $y=mx+b$

Answer:

$y=5x+15$