# Write the equation of the line passing through each of the given pairs of points ~(2,-3) and...

## Question:

Write the equation of the line passing through each of the given pairs of points {eq}~(2,-3) {/eq} and {eq}~(2,4). {/eq} Express it in slope-intercept form.

## Answer and Explanation:

The given points are:

$$(x_1, y_1)= (2, -3) \\ (x_2, y_2)= (2, 4)$$

The slope of the line through these points is calculated by using:

\begin{align} m&= \dfrac{y_2-y_1}{x_2-x_1} \\ &= \dfrac{4-(-3)}{2-2} \\ &= \dfrac{7}{0} \\ &= \text{Undefined} \end{align}

Since the slope of the line is undefined, it is vertical.

So the equation of this line is of the form {eq}x=k {/eq}.

This passes through the point {eq}(x, y)= (2, -3) {/eq}.

Substitute these values in the above equation:

$$2=k$$

Substitute this back into the same equation back:

$$\boxed{\mathbf{x=2}}$$