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Chapter 3: Q. 3.46 (page 273)

Use slopes to determine if the lines are perpendicular:

鈸� y=2x-5and x+2y=-6

鈸� 2x-9y=3and 9x-2y=1

Short Answer

Expert verified

鈸� The given lines are perpendicular.

鈸� The given lines are not perpendicular.

Step by step solution

01

Step 1. Given Information  

Pair of lines:

鈸� y=2x-5and x+2y=-6

鈸� 2x-9y=3and 9x-2y=1

02

Step 2. Required to find  

Use slopes to determine if the lines are perpendicular.

03

Step 3. Convert the equations into slope and y-intercept form 

If the co-efficient of y is not 1, divide the equations by the co-efficient of y, rearrange the terms to make equation of the form y=mx+b.

the equations become:

鈸� y=2x-5and y=-12x-3

鈸� y=29x-13and y=92x-12

04

Step 4. Use the slopes to check perpendicularity 

The slopes are negative reciprocals of each other, to be perpendicular. We multiply the slopes and check for product to be equal to -1:

鈸� m1脳m2=2脳-12=-1. Therefore, the given lines are perpendicular.

鈸� m1脳m2=29脳92=1. Therefore, the given lines are not perpendicular.

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