Question

1. write the equation of a line that passes through (-4,5) and is parallel to y = 6x + 8.

Explanation:

Step1: Identify parallel line slope

Parallel lines have equal slopes. For $y=6x+8$, the slope $m=6$.

Step2: Use point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$. Substitute $m=6$, $x_1=-4$, $y_1=5$.
$y - 5 = 6(x - (-4))$

Step3: Simplify to slope-intercept form

Simplify the right-hand side and solve for $y$:
$y - 5 = 6(x + 4)$
$y - 5 = 6x + 24$
$y = 6x + 24 + 5$
$y = 6x + 29$

Answer:

$y = 6x + 29$