Question

The description below represents Function A and the table represents Function B: Function A The function is 8 more than 3 times x. Function B x y −1 2 0 5 1 8 Which statement is correct about the slope and intercept of the two functions? (1 point) Their slopes are equal but y-intercepts are not equal. Their slopes are not equal but y-intercepts are equal. Both slopes and y-intercepts are equal. Neither slopes nor y-intercepts are equal.

Answer 1

Answer: first option, their slopes are equal but y-intercepts are not equal.

Justification:

1) Function A

The function is 8 more than 3 times x. => y = 8 + 3x

2) Function B

x y

−1 2

0 5

1 8

3) Slope and y intercept of y = 8 + 3x

That equation is the slope - intercept form of the line.

The general equation is y = mx + b, where m is the slope and b is the y-intercept.

So, in y = 8 + 3x, the slope is 3 and the y-intercept is 8

4) slope of the function B:

slope = rise / run = Δy / Δx

slope = [5 - 2] / [ 0 - (-1) ] = 3 / 1 = 1

Also, slope = [ 8 - 5] / [1 - 0] = 3 / 1 = 3

Also, slope = [ 8 - 2] / [1 - (-1)] = 6 / 2 = 3

So, definetly the points represent a linear function with slope 3.

The y-intercept is the value of y when x = 0. From the table y = 5 when x = 0, so the y - intercept is 5.

5) Summarizing:

Function slope y - intercept

A 3 8

B 3 5

From which you conclude that: their slopes are equal but y-intercepts are not equal.