Please help

The line passes through the points

(2,3) and (4,7)

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