Math Destroyer Test 4 Q # 24

[wired202808]

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Which of the following is the equation OF THE LINE that contains the point (2, -1,) and is perpendicular to the line y=-4x+5? The answer in the book is y=(1/4)x - 3/2, but there is no solution, can someone please explain?

 

[OhioDMD]

Which of the following is the equation OF THE LINE that contains the point (2, -1,) and is perpendicular to the line y=-4x+5? The answer in the book is y=(1/4)x - 3/2, but there is no solution, can someone please explain?

In order for two lines to be perpendicular to one another their slopes
must be negative recipricals. The slope of the given line is -4 therefor
the perpendicular line must have a slope of 1/4. in its simplist form

y= 1/4x plus or minus a constant

by substituting the (x,y) values the two must share you get

y= 1/4x -3 as the needed equation .... the answer in the book is wrong 😳(

 

[DevinD]

Actually, the answer in the book is right.

For lines that are perpendicular to each other, their slopes multiply to equal -1. E.g. if line A has slope (m) = 2, line B (which is perpendicular to line A) has slope = -1/2.

Check:
2(-1/2) = -1

So y= -4x + 5 (equation in problem)
Slope of equation perpendicular to this equation = 1/4
To get the second equation, set up the point system (I think that's what you call it 🙂)
y-y1 = m (x-x1)
y+1=1/4(x-2).......I'm gonna skip some work steps 😀
y=(1/4)x -3/2

Hope this helps

 

[wired202808]

thanks Ohio, appreciate it!

 

[ToBeDDSS]

Btw there is an easy way. dont need to do the whole thing as long as you know the relationship between the slopes of 2 perpendicular lines.
(m1=-1/m2)
the slope of the line is -4 so the slope of the perpendicular line is 1/4. there is only one choice and that's ur answer

 

[wired202808]

thanks ToBe that helps!