Question

triangle abc is similar to triangle def. write the equation, in slope - intercept form, of the side of triangle def that is parallel to $overline{bc}$. you must show all work to receive credit.

Explanation:

Step1: Find slope of $\overline{BC}$

Let $B(-2,4)$ and $C(2,1)$. Slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{1 - 4}{2-(-2)}=-\frac{3}{4}$.

Step2: Use point - slope form with point $E(4,4)$

Parallel lines have same slope. Using $y - y_1=m(x - x_1)$ with $m = -\frac{3}{4}$ and $(x_1,y_1)=(4,4)$ gives $y - 4=-\frac{3}{4}(x - 4)$.

Step3: Convert to slope - intercept form

$y-4=-\frac{3}{4}x + 3$, so $y=-\frac{3}{4}x+7$.

Answer:

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