Question

The table below represents a linear function for the cost of a gym membership based on the number of months of membership.

Time (month) Cost
1 $105
3 $165
5 $225
7 $285
What is the slope and y-intercept of the linear function?

The slope is ____ and the y-intercept is ___.

Answer 1

The slope is 30, and the y-intercept is 75.

Explanation:

Use two points from the table, and find the equation of a line given two points.

Point 1: (1, 105)

Point 2: (3, 165)

y = mx + b

slope = m = (y_1 - y_1)/(x_2 - x_1)

m = (165 - 105)/(3 - 1) = 60/2 = 30

y = 30x + b

Use point (1, 105) for x and y.

105 = 30(1) + b

105 = 30 + b

b = 75

y = 30x + 75

The slope is 30, and the y-intercept is 75.