Question

in the function above, the slope will be multiplied by -4, and the y-value of the y-intercept will be decreased by 1 unit. which of the following graphs best represents the new function?

Explanation:

Step1: Identify original function

First, take graph W (the original function): it crosses y-axis at $(0,-2)$, so y-intercept $b=-2$. Slope $m=\frac{\text{rise}}{\text{run}}=\frac{3}{1}=3$. Original function: $y=3x-2$.

Step2: Transform slope

Multiply slope by -4: $m_{\text{new}}=3\times(-4)=-12$.

Step3: Transform y-intercept

Decrease y-intercept by 1: $b_{\text{new}}=-2-1=-3$.

Step4: New function & properties

New function: $y=-12x-3$. It has a negative steep slope, y-intercept at $(0,-3)$.

Answer:

Z. The graph with a steep negative slope and y-intercept at (0,-3)