   Chapter 1, Problem 53RE

Chapter
Section
Textbook Problem

Find an equation of the line that passes through the point (−2, −4) and is perpendicular to the line with equation 2x − 3y − 24 = 0.

To determine
The equation of the lines passing through given point (2,4) and perpendicular to the line 2x3y24=0 .

Explanation

Given:

The equation of the line is 3x+2y+14=0 (1)

Formula used:

Formula to determine the equation of line is,

(yy1)=m2(xx1) (2)

Where,

• (x,y) is the coordinate of point lie on the line.

If two lines are perpendicular to each other then the product of their slopes is equal to 1 .

m1×m2=1 (3)

Where,

• m1 is the slope of given line
• m2 is the slope of line for which we have to find the equation.

Calculation:

To find the value of m1 first it right in the form of slope equation and thjen compare it with the standard slope equation y=mx+c .

Now from equation (1) we can write that y=23x8 on comparing it with the standard form of equation we get m1=23

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