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Chapter 4: Q. 477 (page 540)

In the following exercises, find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope鈥搃ntercept form.

line 4x+5y=-3, point0,0

Short Answer

Expert verified

The equation of the line isy=54x.

Step by step solution

01

Step 1. Given Information 

We are given the line 4x+5y=-3and point0,0. We need to find the line perpendicular to the given line.

02

Step 2. Finding the perpendicular line 

The slope-intercept form of given line is:

4x+5y=-3鈬�5y=-3-4x鈬�y=-4x5+-35鈬�y=-45x-35

Slope of given line=-45

The slope of the perpendicular line is the negative reciprocal of the slope of the given line.

Therefore, slope of perpendicular line54

The equation of the perpendicular line with the slope 54and point 0,0is:

y-y1=mx-x1鈬�y-0=54x-0鈬�y=54x

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