Question

line c has an equation of $y = -\frac{3}{4}x - 3$. line d, which is parallel to line c, includes the point $(-2, -2)$. what is the equation of line d?
write the equation in slope - intercept form. write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

Explanation:

Step1: Determine slope of line d

Parallel lines have equal slopes. Line c has slope $-\frac{3}{4}$, so line d also has slope $m = -\frac{3}{4}$.

Step2: Use point - slope form

Point - slope form is $y - y_1 = m(x - x_1)$, where $(x_1,y_1)=(-2,-2)$ and $m = -\frac{3}{4}$.
Substitute values: $y - (-2)=-\frac{3}{4}(x - (-2))$
Simplify: $y + 2=-\frac{3}{4}(x + 2)$

Step3: Convert to slope - intercept form

Expand the right - hand side: $y+2 = -\frac{3}{4}x-\frac{3}{4}\times2$
$y + 2=-\frac{3}{4}x-\frac{3}{2}$
Subtract 2 from both sides: $y=-\frac{3}{4}x-\frac{3}{2}-2$
Convert 2 to $\frac{4}{2}$: $y = -\frac{3}{4}x-\frac{3}{2}-\frac{4}{2}$
$y=-\frac{3}{4}x-\frac{7}{2}$

Answer:

$y = -\frac{3}{4}x-\frac{7}{2}$