Slope: Practice

Apply the slope formula, watching the negative coordinate.

$m = \frac{10 - 2}{3 - (-1)} = \frac{8}{4} = 2$

So the slope is $2$.

Apply the slope formula and simplify.

$m = \frac{1 - (-1)}{2 - (-2)} = \frac{2}{4} = \frac{1}{2}$

So the slope is $\tfrac{1}{2}$.

Take $(4, -2)$ as point one and $(1, 7)$ as point two.

$m = \frac{7 - (-2)}{1 - 4} = \frac{9}{-3} = -3$

So the slope is $-3$.

Both points have the same height, $y = 4$, so the rise is zero.

$m = \frac{4 - 4}{5 - (-3)} = \frac{0}{8} = 0$

So the slope is $0$ (a horizontal line).

Both points have the same $x$-coordinate, $x = 2$, so the run is zero.

$m = \frac{3 - (-5)}{2 - 2} = \frac{8}{0}$

Dividing by zero has no value, so the slope is undefined (a vertical line).

Read $\tfrac{3}{4}$ as a run of $4$ and a rise of $3$. Step right $4$ and up $3$ from $(1, 2)$.

$(1, 2) \longrightarrow (1 + 4,\; 2 + 3) = (5, 5)$

So $(5, 5)$ is on the line.

Apply the slope formula and simplify.

$m = \frac{0 - (-2)}{0 - (-4)} = \frac{2}{4} = \frac{1}{2}$

So the slope is $\tfrac{1}{2}$.

Compare the sizes of the slopes, ignoring sign.

$|-3| = 3 \quad\text{and}\quad |2| = 2$

Since $3 > 2$, the slope $-3$ line is steeper, even though $-3$ is the smaller number.

Take $(6, 1)$ as point one.

$m = \frac{3 - 1}{2 - 6} = \frac{2}{-4} = -\frac{1}{2}$

So the slope is $-\tfrac{1}{2}$.

Read $-2$ as $\tfrac{-2}{1}$: a run of $1$ and a rise of $-2$. Step right $1$ and down $2$ from $(0, 5)$.

$(0, 5) \longrightarrow (0 + 1,\; 5 - 2) = (1, 3)$

So $(1, 3)$ is on the line.

Apply the slope formula.

$m = \frac{6 - 0}{-2 - 0} = \frac{6}{-2} = -3$

So the slope is $-3$.

Slope is rise over run, keeping the signs.

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

So the slope is $-4$.