Question

For questions 1-8, read and solve each problem; choose the best answer from the choices provided

for each item.
1. (MGSE9-12.F.BF.1) This table shows the number of people at a festival at certain times during
the day. Which function best represents the table below?
Hour (PM) 1 2 4 7 8
Number of People 12 19 33 54 61
A. f(x) = 7x + 12
B. f(x) = 7x + 5
C. f(x) = 5x + 7
D. f(x) = 5x + 12

Answer 1

`f(x) = 7x + 5`.

Explanation:

The equation that represents the function can be written in the slope-intercept form,
`f(x) = mx + b`.

To create an equation, we need to find the slope (m) and the y-intercept (b) of the function.

First, calculate the slope of the function using two points, (1, 12) and (2, 19).

`slope (m) = (y_2 - y_1)/(x_2 - x_1) = (19 - 12)/(2 - 1) = (7)/(1) = 7`

Next, find b by substituting x = 1, f(x) = 12, and m = 7 into
`f(x) = mx + b`.

`12 = (7)(1) + b`

`12 = 7 + b`

Subtract 7 from each side

`12 - 7 = b`

`5 = b`

`b = 5`

Substitute m = 7 and b = 5 into
`f(x) = mx + b`.

✅Thus, the equation that represents the function would be:

`f(x) = 7x + 5`.