Precalculus Examples

$(\frac{7}{3}, - 8)$ , $(\frac{7}{3}, 1)$

Step 1

Find the slope of the line between $(\frac{7}{3}, - 8)$ and $(\frac{7}{3}, 1)$ using $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ , which is the change of $y$ over the change of $x$ .

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Step 1.1

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

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

Step 1.2

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).

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

Step 1.3

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

$m = \frac{1 - (- 8)}{\frac{7}{3} - (\frac{7}{3})}$

Step 1.4

Simplify.

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Step 1.4.1

Combine the numerators over the common denominator.

$\frac{1 - (- 8)}{\frac{7 - 7}{3}}$

Step 1.4.2

Simplify the expression.

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Step 1.4.2.1

Subtract $7$ from $7$ .

$\frac{1 - (- 8)}{\frac{0}{3}}$

Step 1.4.2.2

Divide $0$ by $3$ .

$\frac{1 - (- 8)}{0}$

Step 1.4.2.3

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

Undefined

$\frac{1 - (- 8)}{0}$

Step 1.4.3

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

Undefined

Step 2

The slope of the line is undefined, which means that it is perpendicular to the x-axis at $x = \frac{7}{3}$ .

$x = \frac{7}{3}$

Step 3