HELP PLEASE! Triangle ABC is similar to triangle DEF. Write the equation, in slope-intercept form, of the side of triangle DEF that is parallel to segment BC. You must show all work to receive credit.

y= -1x + 8

Step-by-step explanation:

so we have to know that the side of Triangle DEF that is parallel segment BC is  EF.  

we know that the side EF contains the coordinates (4,4) and (6,2).

So we could use this to find the slope for side EF by finding the difference in the y values and dividing it by the difference in the x values.

4-2= 2

4-6= -2

2/-2= -1  so the slope is negative one.

Now we have to find the y-intercept so we could plot in the x  and y values and the slope into the equation    y=mx + b to find the y-intercept.

In the coordinates (6,2)  6 is the x value and 2 is the y value.

so we put it like this   2=-1(6) + B where -1 is the slope.

2= -6 + b  add 6 to both sides and  b= 8.

so now we know the slope and the y-intercept so we will write the equation like this.    y= -1x + 8

Match each polynomial with its factorization.

Step-by-step explanation:

Side BC: y= -x+2

Side EF : y= -x+8

Explanation:

To set up this equation, first we need to find the slope of . We can do this by simply looking at the graph or using our slope formula since we know the coordinates of B and C. 

B(-2,4) and C(1,1)

m=

Then we would do the same for side  Since it is parallel to side . 

E(4,4) and F(6,2)

m= 

Since, parallel lines share the exact same slope Side BC and Side EF are parallel to each other. Now the equation who consists of the same slope of -1 or -x. 

Since, I know both slopes are -1 I can use point-slope form to then find the y-intercept or b. For Side BC I would plug in coordinate B for my point-slope form and then get my slope intercept form with my slope and y-intercept. 

Point-Slope Form: 

B(-2,4) I would plug these coordinates in point-slope form to then get my slope intercept.

E(4,4) I would plug these coordinates in point slope form to get my slope intercept.

So the equation for EF is y=-x+8 which is parallel to BC which has the equation of y=-x+2.

Hope this helps!