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Chapter 4: Q. 645 (page 571)

In the following exercises, use slopes and y-intercepts to determine if the lines are perpendicular.

3x-2y=5;2x+3y=6

Short Answer

Expert verified

The lines are perpendicular.

Step by step solution

01

Step 1. Given Information 

The given equation of lines are,

3x-2y=52x+3y=6

02

Step 2. Calculating the slope and intercept for one line

The equation can be written as,

3x-2y=52y=3x-5y=32x-52m1=32Intercept=-52

03

Step 3. Calculating the slope and intercept for other line  

The equation can be written as,

2x+3y=63y=-2x+6y=-23x+63m2=-23

04

Step 4. Conclusion 

We observe that,

32路-23=-1m1路m2=-1

Hence, the lines are perpendicular.

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Most popular questions from this chapter

In the following exercises, plot each point in a rectangular coordinate system and identify the quadrant in which the point is located.

鈸� (鈭�4,2)鈸� (鈭�1,鈭�2)鈸� (3,鈭�5)鈸� (鈭�3,5) 鈸�(53,2)

In the following exercises, find the equation of a line with a given slope and y-intercept. Write the equation in slope-intercept form.

388.slope 6and y-intercept (0,-4).

Which of the following ordered pairs are solutions to the equationy=-2x+6?

(a)(0,6)(b)(1,4)(c)(-2,-2)

Find the intercepts for2x+3y=6

In the following exercise, name the ordered pair of each point shown in the rectangular coordinate system :
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