Chapter 4.1, Problem 63HP

To determine

Whether the equation of a vertical line can be written in slope-intercept form

Answer to Problem 63HP

No.

Explanation of Solution

Let us assume the equation of a vertical line

  $x=2$

Formula Used:

Equation of slope-intercept form of a line is given by:

  $y=mx+b\mathrm{............................}(1)$

Where

  $\begin{array}{l}b=y-\mathrm{int}ercept\\ m=\frac{rise}{run}=slope=\frac{y_2-y_1}{x_2-x_1}\mathrm{................}[if(x_1,y_1)\&(x_2,y_2)lie\_on\_line]\end{array}$

Calculation:

Choose any two points on the line $x=2$ .

(2,0) , (2,1) and find the slope of the line.

  $\begin{array}{l}slope=\frac{y_2-y_1}{x_2-x_1}\mathrm{................}[if(x_1,y_1)\&(x_2,y_2)lie\_on\_line]\\ \Rightarrow slope=\frac{1-0}{2-2}\mathrm{...............}[(x_1,y_1)=(2,0)\&(x_2,y_2)=(2,1)]\\ \Rightarrow slope=\frac{1}{0}\end{array}$

The slope is infinite. So, the slope is not defined for vertical line .

Hence, vertical line cannot be written in slope-intercept form.

Graph:

Plot the points with x value =2 and y value can be any.

Let us plot (2,0) , (2,1) and join these points to get the graph of the equation.