Question

. Open Response 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.

Answer 1

To write the equation of the function in the form y = mx + b, use the given information to set up a system of equations and solve for m and b.

Step-by-step explanation:

To write the equation of the function in the form y = mx + b, we need to find the values of m and b.

Let x represent the number of movies and y represent the total cost. We are given that the total cost for 5 movies is $40 and the total cost for 12 movies is $75.

Using the given information, we can set up a system of equations:

5m + b = 40

12m + b = 75

Subtracting the first equation from the second equation, we get:

12m + b - (5m + b) = 75 - 40

7m = 35

Dividing both sides of the equation by 7, we find:

m = 5

Substituting the value of m back into one of the original equations, we can solve for b:

5(5) + b = 40

25 + b = 40

Subtracting 25 from both sides, we get:

b = 15

Therefore, the equation of the function is y = 5x + 15.

Answer 2

Answer: y = (35/7)x + 15

Step-by-step explanation:

To write the equation of the function in the form y = mx + b, we need to find the slope (m) and the y-intercept (b) of the line.

To find the slope (m), we can use the point-slope formula:

m = (y2 - y1) / (x2 - x1)

We know that the total cost for 5 movies is $40, and the total cost for 12 movies is $75. So, using these two points:

(x1, y1) = (5, 40) and (x2, y2) = (12, 75)

we can plug them into the point-slope formula:

m = (75 - 40) / (12 - 5) = 35/7

To find the y-intercept (b), we can use the slope-intercept formula:

y = mx + b

We know that the y-intercept is the point where the line crosses the y-axis. In this case, when x = 0, the equation becomes y = m(0) + b = b, so b = y-intercept

We have the equation of the function in the form y = mx + b is

y = (35/7)x + b

We can use one of the points (5,40) to find the value of b by substituting it into the equation:

40 = (35/7) * 5 + b

Solving for b, we get:

b = 40 - (35/7) * 5 = 40 - 25 = 15

Therefore, the equation of the function in the form y = mx + b is:

y = (35/7)x + 15

This equation represents the total cost for a reward program member to see x number of movies.