Question

If you are finding the line perpendicular to x + 3y = 5, what is the slope of the line?
Answer

-3/5

1/3

3

-3

Answer 1

Solve your equation for \(y\) to get it in slope-intercept form: \(y = mx+b\) where \(m\) is slope. Now divide -1 by \(m\) to get the slope of the perpendicular line. The product of the slopes of perpendicular lines should equal -1 (unless one of them is vertical)

Answer 2

How would you divide m?

Answer 3

\(m\) is going to be a number. I'll walk you through it. Solve the equation for \(y\): what do you get?

Answer 4

What is y again is the answer -1

Answer 5

Come on, you have the equation
\[x +3y = 5\]
Solve that for \(y\). In other words, arrange it so \(y = \) <something>

Answer 6

Do you know how to do that?

Answer 7

\[x+3y=5\]Subtract \(x\) from both sides:
\[x-x+3y = 5-x\]\[3y=5-x\]Divide both sides by 3:
\[\frac{3y}{3} = \frac{5-x}{3}\]\[y=-\frac{1}{3}x+\frac{5}{3}\]

Answer 8

Now, compare that with slope intercept form: \[y=mx+b\]

Matching up the respective pieces, what is the value of \(m\)?

Answer 9

ok would you add 1/3x + 5/3 to get m?

Answer 10

\[y = mx + b\]
\[y = -\frac{1}{3}x + \frac{5}{3}\]

Match up the pieces! \(y\) matches \(y\). what matches with \(mx\)?

Answer 11

-1/3

Answer 12

Yes, \[m = -\frac{1}{3}\]

Okay, the slope of the other line is \[\frac{1}{m} = \frac{1}{-\frac{1}{3}}=\]

Do you know how to divide fractions?

Answer 13

do you flip the fraction and multiply it?

Answer 14

Flip the fraction in the denominator and multiply by it, yes.

Answer 15

so that would be 1/m times -1/3/1

Answer 16

-1/3/m

Answer 17

no.

we are trying to divide 1 by -1/3.

1 = 1/1
invert -1/3 -> -3/1
1/1 * -3/1 = -3

Answer 18

Ah, @#$#$, we wanted to divide -1 by m, not 1. Sigh.

\[\frac{-1}{m} = \frac{-1}{-\frac{1}{3}}\]to do that, we multiply the numerator (-1) by the inverted denominator (-3/1)
\[-1*\frac{-3}{1} = 3\]

Answer 19

okay that makes sense I did not know that

Answer 20

We need the two slopes to multiply together and give -1 as the answer. Let's see if they do:

\[-\frac{1}{3}*3=-\frac{3}{3} = -1\]They do, so 3 is the correct answer for the slope of the perpendicular line.

Answer 21

Sorry for the confusion due to the missing - sign! This is an example of why I always check my work — I catch silly mistakes like this!

Answer 22

okay great tip " to always check your work"
Thank you so much for the help

Answer 23

Hope it helped!

Answer 24

Another thing - slope of a perpendicular line follows the format \[m= -\frac{1}{m}\] where -1/m is the slope of the perpendicular line and m is the slope of the line given/found.