Question

use the given conditions to write an equation for the line in point - slope form and in slope - intercept form. passing through (-8, -2) and parallel to the line whose equation is y = -4x + 2
write an equation for the line in point - slope form.
( simplify your answer. use integers or fractions for any numbers in the equation. )
write an equation for the line in slope - intercept form.
( simplify your answer. use integers or fractions for any numbers in the equation. )

Explanation:

Step1: Identify parallel line slope

Parallel lines have equal slopes. The given line $y=-4x+2$ has slope $m=-4$.

Step2: Write point-slope form

Use point $(-8,-2)$ and $m=-4$ in $y-y_1=m(x-x_1)$.
$y - (-2) = -4(x - (-8))$
Simplify signs: $y+2=-4(x+8)$

Step3: Convert to slope-intercept form

Expand the right-hand side:
$y+2=-4x-32$
Subtract 2 from both sides:
$y=-4x-32-2$
Combine constants: $y=-4x-34$

Answer:

Point-slope form: $y+2=-4(x+8)$
Slope-intercept form: $y=-4x-34$