Question

Triangle ABC is similar to triangle DEF. Wrote the equation, in slopeIntercept form, of the side of triangle DEF that is parallel to BC. You must show all work to receive credit

Answer 1

To find the slope intercept form equation of the side that is parallel to BC (which is EF), the first step is to find the slope of the line, to do it, we have to use the coordinates of the given 2 points in the following formula:

$m=\frac{y2-y1}{x2-x1}$

These 2 points are E(4,4) and F(6,2):

$m=\frac{2-4}{6-4}=-\frac{2}{2}=-1$

The slope of the equation is -1.

Now, we can use one of the given points and the slope to find the intercept form by using the point slope formula:

$\begin{gathered} y-y1=m(x-x1) \\ y-4=-1(x-4) \\ y-4=-x+4 \\ y=-x+4+4 \\ y=-x+8 \end{gathered}$

The equation of the segment is y=-x+8.