Question

use the given conditions to write an equation for the line in point - slope form and in slope - intercept form.
passing through (-3, -7) and parallel to the line whose equation is y = -4x + 5
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. For $y=-4x+5$, slope $m=-4$.

Step2: Write point-slope form

Use point $(-3,-7)$ and $m=-4$. Point-slope formula: $y-y_1=m(x-x_1)$
$y-(-7)=-4(x-(-3))$
Simplify: $y+7=-4(x+3)$

Step3: Convert to slope-intercept form

Expand the right side:
$y+7=-4x-12$
Subtract 7 from both sides:
$y=-4x-12-7$
$y=-4x-19$

Answer:

Point-slope form: $y+7=-4(x+3)$
Slope-intercept form: $y=-4x-19$