# Thread: find equation of line

1. ## find equation of line

Cant solve this problem. Have and exam coming very soon.

Write down the equation of any line through the point (-4, 2)
Hence find the equations of the two lines through the point (-4, 2) whose perpendicular distance from the origin is 2.

2. This is for a geometry class?? Sounds more like Algebra 2 or maybe the beginning of a pre-calc/college algebra course. Nonetheless, follow below:

You want the equation of any line that goes through (-4, 2).

Let's make it simple: set up y = mx + b and we can even for your own convenience let m be 1. Thus, y = x + b is appropriate. Lets plug in -4 as our x-coord and 2 as our y-cord. We now have: 2 = -4 + b

In this case, (and there are infinitely many), 2 = -4 + 6, so:

y = x + 6 is an equation that goes through (-4, 2).

-Andy

3. Thanks but you did not answer the second part of the question. In know the first part.

4. i get one line within 1 second.....
y=2
lol....

5. the other one i get is y=-4/3x-10/3
i list a three unknown equation
the line pass through -4,2 _so 2=-4m+b let b write as m_ b = 2+4m
the first equation is y=mx+2+4m
the question said the distance from the origin to the line is 2, so let's draw a line through the origin that can be perpendicular the line
-any line pass through the origin can be write as y=mx
-if two lines are perpendicular to each other, their slopes have a productof -1
so the second equation is y=-1/mx(-1/m compare to the line we need to calculate)
third the the vertical distance from the origin to the line is 2
so we can write it as x^2+y^2=2^2
now we have three equations with three unknows
y=mx+2+4m
y=-1/mx
x^2+y^2=2^2
then solve for the equation. i get x= -8/5 and y= -6/5
then solve the equation pass through 2 points (-4,2),(-8/5, -6/5)
i don't know if i get the right equation, but i'm pretty sure i use the right method....
i hope this helps, can somebody confirm my answer , thank you