Question

the equation for line c can be written as $y = -\frac{6}{7}x - 1$. line d is parallel to line c and passes through (10, -9). 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 $c$: $y = -\frac{6}{7}x - 1$, slope $m = -\frac{6}{7}$.

Step2: Use point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$. Substitute $m = -\frac{6}{7}$, $x_1=10$, $y_1=-9$:
$y - (-9) = -\frac{6}{7}(x - 10)$

Step3: Simplify to slope-intercept form

First rewrite left side: $y + 9 = -\frac{6}{7}x + \frac{60}{7}$
Subtract 9 (which is $\frac{63}{7}$) from both sides:
$y = -\frac{6}{7}x + \frac{60}{7} - \frac{63}{7}$
$y = -\frac{6}{7}x - \frac{3}{7}$

Answer:

$y = -\frac{6}{7}x - \frac{3}{7}$