You have the following points:
(7,r)
(1,-1)
and you have to find the value of r, that makes that the line which crosses the previous points has a slope of m = 1/2.
To find the value of r, you use the following formula for the slope m:
m = (y2 - y1)/(x2 - x1)
where (x1,y1) and (x2,y2) are two point of the line.
The points are:
(x1,y1) => (1,-1)
(x2,y2) => (7,r)
replace the previous values in the formula for the slope m, and solve for r:
m = (r - (-1))/(7 - 1)
m = (r + 1)/(6) multiply both sides by 6
6m = r + 1 subtract both sides by 1
6m - 1 = r replace the value of m = 1/2
6(1/2) - 1 = r
3 - 1 = r
2 = r
Hence, the value of r has to be r = 2 for getting a slope of m = 1/2 of a line which crosses the given points