Find the Equation Using Point-Slope Formula (3,5) , (3,1)

$(3, 5)$ , $(3, 1)$

Step 1

Find the slope of the line between $(3, 5)$ and $(3, 1)$ using $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ , which is the change of $y$ over the change of $x$ .

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.

$m = \frac{1 - (5)}{3 - (3)}$

Simplify.

Multiply $- 1$ by $3$ .

$\frac{1 - (5)}{3 - 3}$

Subtract $3$ from $3$ .

$\frac{1 - (5)}{0}$

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 $x = 3$ .

$x = 3$

Step 3

Find the Equation Using Point-Slope Formula (3,5) , (3,1)

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