Write the slope-intercept equation for the line that passes through (2,-3) and is perpendicular to x-2y=5

Question

anonymous · Answer

Now what do you know about perpendicular lines? esp. their slopes?

anonymous · Answer

They have 90 degree angles

anonymous · Answer

and are negative reciprocals of each other

anonymous · Answer

right!

well, the slope of x-2y=5 is -a/b, which is -(1/-2)=1/2
 so we would take the negative reciprocal of 1/2 which is -2.

-2(2)+b=-3
-4+b=-3
b=3/4 which is our y-int.

so our equation is y= -2x+3/4

anonymous · Answer

Thanks, my answer key states the right answer is y= -2x+1?

anonymous · Answer

oh whoops. yes. from -4+b=-3 I accidently divided. it is -3+4=1
so indeed it is -2x+1.

sorry about that

anonymous · Answer

Thank you so much !

anonymous · Answer

Where did you get the positive 2 that you multiplied from the -2?

anonymous · Answer

you take the given coordinate (2,-3) and substitute into the x and  of:

-2x+b=y

then you solve for b. (2,-3) is a part of the line, and we know it should have a slope of -2. so now what we had left to do was solve for  b, or the y-intercept. 

Then once we have b and the slope, it can become a function, ready to accept any given x-value to put out a yvalue. these values are on the line

anonymous · Answer

Thank you!  I've got it now.  Can't thank you enough!

anonymous · Answer

no problem! I really recommend Khan academy's videos, or buying some Art Of Problem Solving workbooks. they're both very helpful.