(-2,r), (6,7), m=1/2. How do you find r?

You have two points, which can be labeled (x_1, y₁) and (x₂, y₂).

The formula for the slope between two points is m = (y₂ - y1 )/(x₂ - x₁).

We can fill in the pieces:

          1/2  =  (7 - r)/(6 - (-2)) 

0r       (7 - r)/(6 + 2) = 1/2

                (7 - r)/8    = 1/2

Now multiply both sides by 8 to clear 8 from the denominator on the left:

                (7 - r)  = 8(1/2)
                     7 - r =  4
                   r = 3

slope is rise over run

so

r-7      =     1

-2-6            2

we start by simplifying as much as we can

r-7   =  1

-8         2

next we get rid of the denominators by cross multiplying. we multiply the bottoms by the tops on the other side of the equation

2(r-7)=-8*1

then simplify

2(r-7)=-8

then we distribute the 2   a(b+c)=ab+ac

2r-2*7=-8

2r-14=-8

then cancel the 14 by adding 14 to both sides

2r-14+14=-8+14

2r=6

then cancel the 2 by dividing both sides by 2

2r/2=6/6

r=3

so r has to be 3

did you understand if you have any questions please comment.