Question

if y = 12x + 7 were changed to y = 12x + 2, how would the graph of the new function compare with the original? a. it would be less steep. b. it would be shifted up. c. it would be steeper. d. it would be shifted down.

Explanation:

Step1: Recall slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. In $y = 12x+7$ and $y = 12x + 2$, the slope $m = 12$ for both lines.

Step2: Analyze y - intercept change

The y - intercept of the first line is $b_1=7$ and of the second line is $b_2 = 2$. Since $2<7$, the change in the y - intercept is $\Delta b=2 - 7=- 5$. A negative change in the y - intercept means a downward shift.

Answer:

D. It would be shifted down.