Chapter 4.3, Problem 9CYU

To determine

To find the equation of line in slope-intercept form.

Answer to Problem 9CYU

  $x=2$

Explanation of Solution

Given:

Line passing through the point $\left(2,3\right)$ and is perpendicular to x-axis.

Concept used:

Parallel lines have same slope.

Equation of a line passing through the point $\left(x_1,y_1\right)$ with slope m is $y-y_1=m\left(x-x_1\right)$ .

Calculation:

Given that the required line is perpendicular to x-axis.

This implies that the required line must be parallel to y-axis.

Now the slope of y-axis is not defined.

Since the required line is parallel to y-axis, therefore the slope of required line is also not defined.

Hence equation of the line passing through the point $\left(2,3\right)$ with slope not defined is,

  $\begin{array}{l}y-3=\frac{1}{0}\left(x-2\right)\\ \Rightarrow x-2=0\\ \Rightarrow x=2\end{array}$