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: Identify parallel line slope

Parallel lines have equal slopes. For line $c$: $y = -\frac{3}{4}x - 3$, slope $m = -\frac{3}{4}$.

Step2: Use point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$. Substitute $m = -\frac{3}{4}$, $x_1=-2$, $y_1=-2$:
$y - (-2) = -\frac{3}{4}(x - (-2))$
Simplify signs: $y + 2 = -\frac{3}{4}(x + 2)$

Step3: Convert to slope-intercept form

Expand the right-hand side:
$y + 2 = -\frac{3}{4}x - \frac{3}{4} \times 2$
$y + 2 = -\frac{3}{4}x - \frac{3}{2}$
Subtract 2 from both sides (rewrite 2 as $\frac{4}{2}$):
$y = -\frac{3}{4}x - \frac{3}{2} - \frac{4}{2}$
$y = -\frac{3}{4}x - \frac{7}{2}$

Answer:

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