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Chapter 4: Q. 4.112 (page 518)

Use slopes to determine if the lines 2x鈭�9y=3 and9x鈭�2y=1 are perpendicular.

Short Answer

Expert verified

The slopes are not negative reciprocals of each other, so the lines are not perpendicular.

Step by step solution

01

Step 1. Given information.

The given equations are:

2x-9y=39x-2y=1

02

Step 2. Write first equations in slope-intercept form.

The first equation can be written as:

2x-9y=3-9y=-2x+3y=-2x+3-9y=29x-13

03

Step 3. Write second equations in slope-intercept form.

The second equation can be written as:

9x-2y=1-2y=-9x+1y=-9x+1-2y=92x-12

04

Step 4. Determine whether the lines are perpendicular or not.

Compare the slope intercepts forms of the equations with y=mx+b.

For the first equation, m1=29.

For the second equation, m2=92.

If the product of slopes is -1, then the lines are perpendicular.

m1路m2=29路92=1鈮�-1

The slopes are not negative reciprocals of each other, so the lines are not perpendicular.

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