Question

which equation describes the line that passes through the point $(-5, 6)$ and is parallel to the graph of $y=6x+4$?
a $y=-6x-36$
b $y=6x-41$
c $y=-6x+41$
d $y=6x+36$

Explanation:

Step1: Identify parallel line slope

Parallel lines have equal slopes. For $y=6x+4$, the slope $m=6$.

Step2: Use point-slope form

Point-slope formula: $y-y_1=m(x-x_1)$. Substitute $m=6$, $x_1=-5$, $y_1=6$.
$y-6=6(x-(-5))$

Step3: Simplify to slope-intercept form

Expand and solve for $y$:
$y-6=6(x+5)$
$y-6=6x+30$
$y=6x+30+6$
$y=6x+36$

Answer:

D. $y = 6x + 36$