what is the equation of the line that is parallel to the line y - 1 = 4(x + 3) and passes through the point…

Explanation:

Step1: Identify the slope of the given line

The given line is in point - slope form $y - y_1=m(x - x_1)$, where $m$ is the slope. For the line $y - 1=4(x + 3)$, the slope $m = 4$. Parallel lines have the same slope, so the slope of the required line is also $m = 4$.

Step2: Use the point - slope form to find the equation of the new line

The point - slope form is $y - y_1=m(x - x_1)$. We have $m = 4$ and the point $(x_1,y_1)=(4,32)$. Substitute these values into the formula: $y - 32=4(x - 4)$.

Step3: Simplify the equation

Expand the right - hand side: $y - 32=4x-16$. Then add 32 to both sides of the equation: $y=4x - 16+32$, which simplifies to $y = 4x+16$.

Answer:

D. $y = 4x + 16$