Question

A line contains the points (8, 9) and (–12, –7). Using point-slope form, write the equation of the line that is parallel to the given line and that passes through (–5, –15).

Answer 1

For palarell lines, slope are equal.
slope of first line = (y2 - y1)/(x2 - x1) = (-7 - 9)/(-12 - 8) = -16/-20 = 4/5
equation of a line passing through a point is given by: y - y1 = m(x - x1); where (x1, y1) = (-5, -15) and m = 4/5.
Therefore equation of the line is y - (-15) = 4/5(x - (-5))
y + 15 = 4/5(x + 5)

Answer 2

The slope of the line of the line is calculated through the equation,
                        m = (y2 - y1) / (x2 - x1)
Using the first two points in the given,
                        m = (-7 - 9) / (-12 - 8) = 4/5
The line parallel to this has also a slope of 4/5. Through the point-slope form, the equation of the second line is,
                         y - -15 = (4/5)(x - -5)
Simplifying gives the answer of,
                                      y = (4/5)x -11
Eliminating the fraction, 
                                      5y = 4x - 55