Q. 70 - 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 $y=8$

Containing the point $(3,4)$

Step-by-Step Solution

Answer

The equation of line is $x=3$

Step 1. Given information

The perpendicular line is $y=8$

The point is $(3,4)$

Step 2. Finding the slope of line

Firstly, find the slope of a perpendicular line 

$y=8$ is the horizontal line

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

So, slope is 

$m=undefined$

Step 3. Finding the equation of line

The slope of the line is 

$m=undefined$

The point is 

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

When slope is undefined, then equation will always be x-coordinate 

So, the equation of line is 

$x=3$