the equation for line c can be written as y = -\\frac{6}{7}x - 1. line d is parallel to line c and passes…

Explanation:

Step1: Identify the slope

Parallel lines have the same slope. The slope of line $c$ is $-\frac{6}{7}$, so the slope of line $d$ is also $m = -\frac{6}{7}$.

Step2: Use the point - slope form

The point - slope form is $y - y_1=m(x - x_1)$. Given the point $(x_1,y_1)=(10,-9)$ and $m = -\frac{6}{7}$, we have $y-(-9)=-\frac{6}{7}(x - 10)$.

Step3: Simplify to slope - intercept form

First, simplify $y + 9=-\frac{6}{7}(x - 10)$. Distribute the $-\frac{6}{7}$: $y+9=-\frac{6}{7}x+\frac{60}{7}$. Then subtract 9 from both sides. Since $9=\frac{63}{7}$, we get $y=-\frac{6}{7}x+\frac{60}{7}-\frac{63}{7}$, which simplifies to $y = -\frac{6}{7}x-\frac{3}{7}$.

Answer:

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