Question

The points (-7, -1) and (r, 1) lie on a line with slope 1/4

Find the missing coordinater.
r =

Answer 1

r = 1

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.