Slope: Practice

Divide the rise by the run.

$m = \frac{3 - 0}{1 - 0} = \frac{3}{1} = 3$

So the slope is $3$.

Subtract the coordinates in the same order on top and bottom.

$m = \frac{5 - 1}{3 - 1} = \frac{4}{2} = 2$

So the slope is $2$.

Both points have the same height, so the rise is zero.

$m = \frac{4 - 4}{6 - 1} = \frac{0}{5} = 0$

A horizontal line has slope $0$.

Moving right, the height increases, so the rise and run have the same sign.

$m = \frac{\text{positive rise}}{\text{positive run}} > 0$

A line that climbs to the right has a positive slope.

Moving right, the height decreases, so the rise is negative while the run is positive.

$m = \frac{\text{negative rise}}{\text{positive run}} < 0$

A line that falls to the right has a negative slope.

Apply the slope formula.

$m = \frac{7 - 1}{5 - 2} = \frac{6}{3} = 2$

So the slope is $2$.

Slope is rise over run.

$m = \frac{1}{4}$

So the slope is $\tfrac{1}{4}$, a gentle upward tilt.

Slope is rise over run, keeping the sign of the rise.

$m = \frac{-2}{1} = -2$

The negative rise makes the slope $-2$.

The rise is the vertical change between two points, measured by the $y$-coordinates.

$\text{rise} = y_2 - y_1$

So the rise is the change in $y$. The change in $x$ is the run.

Apply the slope formula.

$m = \frac{9 - 3}{4 - 2} = \frac{6}{2} = 3$

So the slope is $3$. The value $6$ is only the rise, not the ratio.

A vertical line never changes its $x$-coordinate, so the run is $0$.

$m = \frac{\text{rise}}{0}$

Dividing by zero has no value, so the slope is undefined.

Slope is rise over run.

$m = \frac{5}{5} = 1$

So the slope is $1$.