Question

which equation represents a line that passes through the point $(6, -3)$ and is parallel to the graph of $y = 3x + 1$?
a. $y = 3x - 21$
b. $y = 3x + 15$
c. $y = -\frac{1}{3}x - 1$
d. $y = -\frac{1}{3}x - 5$

Explanation:

Step1: Identify parallel line slope

Parallel lines have equal slopes. For $y=3x+1$, slope $m=3$.

Step2: Use point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$. Substitute $m=3$, $x_1=6$, $y_1=-3$:
$y - (-3) = 3(x - 6)$

Step3: Simplify to slope-intercept form

Simplify the equation:
$y + 3 = 3x - 18$
$y = 3x - 18 - 3$
$y = 3x - 21$

Answer:

A. $y = 3x - 21$