# Find the equation for a line which goes thorugh origo

#### Anna55

##### New member
Decide the equation for the line which goes through origo and are perpendicular against the line x-y+1=0
Please explain how to solve this. Thank you in advance!

#### Denis

##### Senior Member
Anna55 said:
...perpendicular against the line x-y+1=0
Can you calculate the slope of that line?
If not, you need classroom help.

#### wjm11

##### Senior Member
Decide the equation for the line which goes through origo and are perpendicular against the line x-y+1=0
First, rearrange the equation into y = mx + b (slope-intercept) form. This is to clearly identify "m", the slope.

Once the slope is found, it can be used to find the slope of the perpendicular line; the perpendicular line slope will be the "negative reciprocal" of "m", i.e., -m^(-1). If the original slope is (a/b), the perpendicular to that is -(b/a).

#### mmm4444bot

##### Super Moderator
Staff member
Anna55 said:
Please explain how to solve this.
Here's a step-by-step example, using a different given line.

Find an equation for the line passing through the Origin which is perpendicular to the line 2x + y - 4 = 0.

STEP 1: Determine the slope of the given line, by solving for y

y = -2x + 4

We see by inspection that the slope of this line is -2

STEP 2: Determine the slope of the perpendicular line

The perpendicular slope is the negative reciprocal of -2, which is 1/2.

STEP 3: Use the Point-Slope Formula, to write the equation

y - 0 = 1/2(x - 0)

y = 1/2 x

If you need more help, please ask specific questions or show your work.

#### Anna55

##### New member
Thank you for the help!

x-y+1=0
y=x+1
The slope is 1.
1(x)= -1
x= -1
y= -x

Is my working out correct?

#### mmm4444bot

##### Super Moderator
Staff member

Anna55 said:
x-y+1=0

y=x+1

The slope is 1. Correct

1(x)= -1 You should use symbol m for representing the slope here (symbol x is already used as a variable, in this exercise)

x= -1 This is the correct slope for the perpendicular line

y = -x This final answer is correct

Is my working out correct?

In my example, I suggested that you use the Point-Slope formula.

With experience, we come to realize that the form of all non-vertical lines passing through the Origin is simply y = mx.

If you used y = mx at the end of your exercise, instead of using the Point-Slope form, you are savvy. 