The points (-7, -1) and (r, 1) lie on a line with slope 1/4 Find the missing coordinater.
r =

r = 1

Step-by-step explanation:

Find the missing x-coordinate r.

Use the point-slope formula y - k = m(x - h).  We are given the point (-7, -1) on the line and the slope of the line 1/4, and so this general formula becomes

y + 1 = (1/4)(x + 7)

Now substitute the coordinates of the other point (r, 1) to solve for r:

1 + 1 = (1/4)(r + 7)

Multiplying both sides by 4 eliminates the fractional coefficient:

8 = r + 7

It is readily apparent that r must be 1.

Check:  If r = 1, then (r, 1) becomes (1, 1).  use the point-slope formula again, this time to see if we are correctly predicting the r value 1:

y + 1 = (1/4)(x + 7)  becomes 1 + 1 = (1/4)(r + 7), or

2 = (1/4)(r + 7).  Multiplying both sides by 4, we get 8 = r + 7, and so r = 1.