Question

A line parallel to the graph of (y − 4) = m(x − 7) passes through (−1,−2) and (m, 10). If

m > 0, what is the value of m?

Answer 1

Explanation:

Givens

These are the givens for the second line. The second line also has m (same value) as the x coordinate of one of the points. I'm not sure why you are given the first line.

x1 = - 1

x2 = m

y1 = - 2

y2 = 10

Second line formula for m

m = (y2 - y1) / (x2 - x1) Substitute values for this equation

Solution

Note that the m you seek is both the slope of the second line, and the x coordinate of one of the points.

m = (10 - - 2) / (m - - 1) Change the double minus, and combine

m = 12 / (m + 1) Multiply both sides by (m + 1)

m(m+1) = 12 Remove the brackets

m^2 + m = 12 Subtract 12 from both sides.

m^2 + m - 12 = 0 Factor

(m + 4)(m - 3) = 0

We are told that m >0

So m- 3 = 0

m = 3

Answer

The value for m = 3. The first line also has a slope of 3