Question

1. find the equation of a line parallel to y = 3x - 4 that passes through (6, -7)

Explanation:

Step1: Identify parallel line slope

Parallel lines have equal slopes. For $y=3x-4$, the slope $m=3$.

Step2: Substitute point into slope-intercept form

Use $y=mx+b$, substitute $x=6$, $y=-7$, $m=3$:
$-7 = 3(6) + b$

Step3: Solve for y-intercept $b$

Calculate $3(6)=18$, then rearrange:
$b = -7 - 18 = -25$

Step4: Write final line equation

Substitute $m=3$ and $b=-25$ into $y=mx+b$.

Answer:

$y=3x-25$