Question

Write the equation of the line that passes through the points (4,8) and (-9,5). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.

Answer 1

The equation of a line in point-slope form is:

y - y1 = m(x - x1)

The slope m of a line is given by the following formula:

$m=\frac{y2-y1}{x2-x1}$

In this case, we are given the points (4,8) and (-9,5), then we get:

$m=\frac{5-8}{-9-4}=\frac{-3}{-13}=\frac{3}{13}$

By replacing the value of m into the point-slope equation, we get:

$y-y1=\frac{3}{13}(x-x1)$

By replacing 4 for x1 and 8 for y1, we get:

$y-8=\frac{3}{13}(x-4)$