#### jwolfe890

##### New member
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!

Last edited:

#### MarkFL

##### Super Moderator
Staff member
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

##### New member
-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

##### Super Moderator
Staff member
-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

##### New member
-1/3 after dividing by 3 on both sides

#### MarkFL

##### Super Moderator
Staff member
-1/3 after dividing by 3 on both sides
Yes, correct!

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.

#### jwolfe890

##### New member
y – 1 = -1/3(x – 3)

y = -1/3x + 1

bam!

thank you so much!

#### MarkFL

##### Super Moderator
Staff member
y – 1 = -1/3(x – 3)
This is correct...

$$\displaystyle y-1=-\frac{1}{3}(x-3)$$

y = -1/3x + 1
Careful! A next step could be:

$$\displaystyle y-1=-\frac{1}{3}x+1$$

Now, add 1 to both sides to get:

$$\displaystyle y=-\frac{1}{3}x+2$$