Chapter 1, Problem 29RE

To determine

To find: an equation of the line

Answer to Problem 29RE

The equation of the line is $x=-3$ .

Explanation of Solution

Given:

Point (-3,4)

Calculation:

The slope of a line containing the points $\left(x_1,y_1\right)$ and $(x,y)$ is $m=\frac{y-y_1}{x-x_1}$

The slope of a vertical line is undefined. The slope becomes undefined when there is a divisionby zero. So, the denominator of $m=\frac{y-y_1}{x-x_1}$ is equal to 0.

That means $x$ is equal to $x_1$ .

The vertical line contains the point $(-3,4),$ where $x_1=-3.$ since $x$ is equal to $x_1,x$ will also be -3.

As the slope is undefined, there is no slope-intercept form for the equation.

Therefore, the equation of the line is $x=-3$ .

Conclusion:

Therefore, the equation of the line is $x=-3$ .