Question

Using either the slope formula or rise/run, find the slope of the line
through (3, 2) and (1, -6).

Answer 1

slope = m

$m=\frac{rise}{run}$

"rise" is the number of units you go up(+) or down(-) from each point   (y-axis)

"run" is the number of units you go to the right from each point    (x-axis)

Lines usually go from left to right, so the point furthest to the left will be the starting point, which is (1, -6). To get from point (1, -6) to (3, 2), you go up 8 units and to the right 2 units, so the slope is  $\frac{8}{2}$  which simplifies to 4

Slope formula:

$m=\frac{y_2-y_1}{x_2-x_1}$   Plug in the two points to find the slope

(1, -6) = (x₁, y₁)

(3, 2) = (x₂, y₂)

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{2-(-6)}{3-1}$   (two negative signs cancel each other out and become positive)

$m=\frac{2+(6)}{3-1}$

$m=\frac{8}{2}$

m = 4