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 slope of parallel line

Parallel lines have equal slopes. The given line $y=-4x+5$ has slope $m=-4$.

Step2: Write point-slope form

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

Step3: Convert to slope-intercept form

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

Answer:

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