Finding Point-Slope form of a line that is Perpendicular to One Given! Please help!!

jwolfe890

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Hello, I have this questions:

Given a line with equation 3x - y = 4. Write an equation in point-slope form of the line perpendicular to the given line through the point (3, 1).

So far, I've been able to reduce the equation to slope intercept form y = 3x – 4, but I am very confused on how to write an equation in point-slope form of the line perpendicular to the given line through the point (3, 1).

If you could offer any advice or insight I would be greatly appreciative!! Thank you!
 
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MarkFL

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When two lines are perpendicular, the product of their slopes is -1. So, what must the slope be of the line perpendicular to:

\(\displaystyle y=3x-4\)
 

jwolfe890

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-3x

and then the values from that line are (3, 1) and i would just need to add them into point-slope form?

thank you!
 

MarkFL

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-3x

and then the values from that line are (3, 1) and i would just need to add them into point-slope form?

thank you!
No, that slope isn't correct. When given the line:

\(\displaystyle y=3x-4\)

We see that the slope of this line is 3. So, for the line perpendicular to this one, whose slope we'll call \(\displaystyle m\), we require:

\(\displaystyle 3m=-1\)

So, what is \(\displaystyle m\)?
 

jwolfe890

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-1/3 after dividing by 3 on both sides
 

MarkFL

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-1/3 after dividing by 3 on both sides
Yes, correct! :D

So, now you know the slope of the line, and a point through which the line must pass, so use the point-slope formula to get the equation of the required line. :D
 

jwolfe890

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y – 1 = -1/3(x – 3)

y = -1/3x + 1

bam!

thank you so much!
 

MarkFL

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