The points , −7−9 and , 1r lie on a line with slope 54 . find the missing coordinate r .

The first given point is (-7, -9)
The second given point is (1, r)

The slope of a line can be calculated using the following rule:
m = (y2 - y1) / (x2 - x1)
where:
m is the slope of the line = 54
y2 is the y-coordinate of the second point = r
y1 is the y-coordinate of the first point = -9
x2 is the x-coordinate of the second point = 1
x1 is the x-coordinate of the first point = -7

Substitute with the givens in the above rule to get the value of r as follows:
54 = (r--9) / (1--7)
54 = (r+9) / (1+7)
54 = (r+9) / 8
54*8 = r+9
432 = r+9
r = 432 - 9 = 423