Question

Write the equation of the line that passes through the points (-9,9) and (8, -2).

Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal
line.

Answer 1

y + 2 = (11/17)(x - 8)

Explanation:

Working with the x- and y-components of the given points, we see that the x component increases by 17 and the y-component decreases by 11. Thus, the slope of this line is m = rise / run, or 11/17.

Start with the general point-slope form: y - k = m(x - h) and use the coordinates of the 2nd point for h and k in this equation:

y + 2 = (11/17)(x - 8)

This is based on the point (-2, 8)

and the slope 11/17.

This result is the desired equation in point-slope form. If we wish to reduce this, proceed as follows:

17(y + 2) = 11x - 88, or 17y + 34 = 11x - 88

This last result simplifies to 17y = 11x - 54, or y = (11/17)x -54/17 (which is in slope-intercept form).