Chapter 4, Problem 11CR

To determine

To Write: An equation of line that passes through point $\left(-3,5\right)$ and is parallel to

y- axis.

Answer to Problem 11CR

An equation of line is $x=-3$ option ‘C’ is correct.

Explanation of Solution

Given information:

Line passes through point $\left(-3,5\right)$ and is parallel to y- axis.

Concept and Formula Used:

Point slope form of a line: $y-y_1=m\left(x-x_1\right)$

If line is parallel to y- axis then its slope is equal to undefined i.e. $\frac{1}{0}$

Parallel lines: If lines are parallel then the slopes of lines are equal

Calculation:

The required line is parallel to y- axis. Therefore its slope is equal to undefined i.e.

  $m=\frac{1}{0}$

The required line passes through $\left(-3,5\right)$ and having slope $m=\frac{1}{0}$ . Using point slope form of equation of line

  $\begin{array}{l}y-y_1=m\left(x-x_1\right)\\ \text{where }\left(x_1,y_1\right)=\left(-3,5\right)\&m=\frac{1}{0}\\ y-\left(5\right)=\frac{1}{0}\left(x-\left(-3\right)\right)\\ 0\left(y-5\right)=1\left(x+3\right)\left(\text{Cross multiply}\right)\\ 0=x+3\\ x=-3\end{array}$

Conclusion:

An equation of line is $x=-3$ option ‘C’ is correct.