Q. 69 - Precalculus Enhanced with Graphing Utilities

Question

Find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer.

Perpendicular to the line $x=8$

Containing the point $(3,4)$

Step-by-Step Solution

Answer

The equation of the line is $y=4$

Step 1. Given information

The perpendicular line is $x=8$

The point is $(3,4)$

Step 2. Finding the slope of line

Firstly, find the slope of a perpendicular line 

$x=8$ is the vertical line

Since the perpendicular to the vertical line is always horizontal line and slope of horizontal line will always be zero.

So, slope is 

$m=0$

Step 3. Finding the equation of line

The slope of line is 

$m=0$

The point is 

$(x_1,y_1)=(3,4)$

Apply point-slope formula

$$\begin{gathered} y-4=0(x-3) \\ y-4=0 \\ y=0+4 \\ y=4 \end{gathered}$$