Algebra Examples

$(2, 5)$ , $(2, 12)$

Find the value of the slope.

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Slope is equal to the change in $y$ over the change in $x$ , or rise over run.

$m = \frac{change in y}{change in x}$

The change in $x$ is equal to the difference in x-coordinates (also called run), and the change in $y$ is equal to the difference in y-coordinates (also called rise).

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

Substitute in the values of $x$ and $y$ into the equation to find the slope.

$m = \frac{12 - (5)}{2 - (2)}$

Simplify.

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Multiply $- 1$ by $2$ .

$\frac{12 - (5)}{2 - 2}$

Subtract $2$ from $2$ .

$\frac{12 - (5)}{0}$

The expression contains a division by $0$ . The expression is undefined.

Undefined

Since the slope is undefined, this is a vertical line. Vertical lines have no y-intercept.

No y-intercept

The slope is undefined and there is no y-intercept.

Slope: Undefined

No y-intercept