Question

Write the equation of the line that passes through the points (8,−7) and (−9,7). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.

Answer 1

Answer:

y + 7 = (-14/17)(x - 8)

Step-by-step explanation:

We want the equation of this line in the point-slope form y - k = m(x - h).

We are given two points (8, -7) and (-9, 7), and may arbitrarily choose one of them to serve as the point (h, k) in the point-slope form shown above.  Then the other point is represented by (x, y) in the point slope form shown above:

Let (h, k) be 8, -7) and let (x, y) be (-9, 7).  Then,  y - k = m(x - h) becomes:

7 - (-7) = m(-9 - 8), so that 14 = m(-17), and the slope is thus m = -14/17

The desired equation is then y + 7 = (-14/17)(x - 8) (which is in point-slope form).  

Another way to get this result would be to find m in the usual way:

          rise           14

m = ------------- = --------- = -14/17 (same as before).

           run           -17