Find the distance from (2,-1) to the line y=2x+3.
The answer is 8/5*root5 by the way, but I want to know how to solve.

I used distance formula.
sqrt ( (x-2)^2 + (y+1)^2)
sqrt ( (x-2)^2 + (2x+3+1)^2)
sqrt ( (x-2)^2 + (2x+4)^2)
sqrt (5x^2 + 12x + 20)

When I enter this on my calculator to solve for x, it cannot do it. What should I do next?

Question

Find the distance from (2,-1) to the line y=2x+3.
The answer is 8/5*root5 by the way, but I want to know how to solve.

I used distance formula. 
sqrt ( (x-2)^2 + (y+1)^2)
sqrt ( (x-2)^2 + (2x+3+1)^2)
sqrt ( (x-2)^2 + (2x+4)^2)
sqrt (5x^2 + 12x + 20)

When I enter this on my calculator to solve for x, it cannot do it. What should I do next?

anonymous · Answer

you don't use X

precal · Answer

What kind of calculator are you using?  Are you using the solve feature?

anonymous · Answer

Yes I am usin the solve feature.

precal · Answer

Why don't you use graph paper instead?

anonymous · Answer

I have to use algebraic methods and show my work.

precal · Answer

graphing on graph paper is a way to show your work

anonymous · Answer

Is there a way to answer the problem algebraically?

anonymous · Answer

Well, the line to the other linen willl be perpendicular to it

anonymous · Answer

Assuming you want the shortest distance

precal · Answer

using graph paper is a valid method, then you can count the number of units

anonymous · Answer

Find the equation of a line perpendicular to y=2x+3 and use the distance formula on the intersection

precal · Answer

You could use a point from the equation.  I would graph it to decide what point to use.

You need two ponts for the distance formula

mertsj · Answer

Have you studied the formula for finding the perpendicular to a line through a point?

anonymous · Answer

Well, I'm in Calculus right now, but I don't know how to continue this problem.

precal · Answer

Yep calculus would study that  
Do the normal line

anonymous · Answer

Wouldn't the normal slope be -1/2 ?

anonymous · Answer

-1/2*

anonymous · Answer

$$y+1=\frac{-1}{2}(x-2)$$

anonymous · Answer

$$y=-\frac{1}{2}x$$

mertsj · Answer

You could put the equation in the form Ax+By=C=0 and use this formula:
$$d=\frac{|Am+Bn+C|}{\sqrt{A ^{2}+B ^{2}}}$$
The point is (m,n)

anonymous · Answer

Now set 2x+3=-(1/2)x to find the intersection, then use the distance formula

anonymous · Answer

x = -6/5

anonymous · Answer

Get y now, and use this point in your distance formula

precal · Answer

Mertsj  what formula did you post?  Do you know the name of it?  Just curious

mertsj · Answer

Perpendicular distance from a Point to a Line

precal · Answer

ok  I have not seen that one before.  Good to know

anonymous · Answer

Okay I now have two methods of approaching this problem. Thank you all for helping me. :)