1. ## applied mathematics

find the equation of Line L in standard form L is parallel to Y=1/3X. Both lines are diagonal to each other. The other points are (2,5)

find the equation of Line L in standard form L is parallel to Y=1/3X. Both lines are diagonal to each other. The other points are (2,5)

Find the equation of line L in standard form.

I added the period to make it a sentence.

L is parallel to y = 1/3 x.

I understand this part.

Both lines are diagonal to each other

I don't know what that means.

The other points are (2, 5)

This is just one point.

I'm going to assume you want to find the equation of line L which passes through point (2, 5) and is parallel to y = 1/3 x. Am I close?

If so,

The slope of y = 1/3 x is 1/3. So this means that the slope of any line parallel to it will also be 1/3.

Now use the point-slope form of the general equation to start with, using m = 1/3 and (x1, y1) = (2, 5)

$\displaystyle y-y_1=m(x-x_1)$

$\displaystyle y-5=\frac{1}{3}(x-2)$

$\displaystyle 3y-15=x-2$

$\displaystyle x-3y=-13$ Standard Form

3. ## thanks

find the equation of Line L in standard form L is parallel to Y=1/3X. Both lines are diagonal to each other. The other points are (2,5)

I read 'diagonal' to mean that line L is normal to line Y.

therefore given

$\displaystyle y-y_1=m(x-x_1)$

where

$\displaystyle m=\frac{-1}{\frac{1}{3}}=-3$

then using (2,5)

$\displaystyle y-5=-3(x-2)$

making

$\displaystyle L=-3x-11$