Question

what is the equation of a line that is parallel to y = -4x - 3 and shifted down 3 units?
a. y = -7x - 3
b. y = -4x - 6
c. y = -4x
d. y = -x - 3

Explanation:

Step1: Recall parallel line slope

Parallel lines have the same slope. The given line \( y = -4x - 3 \) has a slope of \( -4 \), so the new line must also have a slope of \( -4 \). This eliminates options A (\( -7 \) slope) and D (\( -1 \) slope).

Step2: Apply vertical shift

A vertical shift down 3 units means we subtract 3 from the y - intercept of the original line. The original y - intercept is \( -3 \). So the new y - intercept is \( -3-3=-6 \). Using the slope - intercept form \( y = mx + b \) (where \( m=-4 \) and \( b = - 6\)), the equation of the line is \( y=-4x - 6 \).

Answer:

B. \( y = -4x - 6 \)