how to solve for B?

Question

find the equation of the line passing through the pints (2,2) (-3,1)

 

i did the y2-y1/x2-x1 and got y=1/5x+b so now what do i do?

Answer 1

You have an equation with x,y, and b in it.  And, you have TWO pairs of (x,y) that are on the line.  Use either one of those for the (x,y) in your equation [you should get the same answer both times] to solve for b.  Put that in place of "b" in your equation.

 

You're starting to get this !!

 

Oh, and once you get an equation, it is really good to check that BOTH of the given (x,y) pairs satisfy the equation [note: many of us are error-prone].

Answer 2

Hi Jared, 

 

I learned something new from my niece who studies in France. Once you figure out the slope (which you did), to figure out what b is in y = mx+ b, take one of the points and replace the x and the y with it. Since you also know m so now you can solve for b.

 

If using (2,2): y = 1/5 x + b would give 2 = 1/5 (2) + b  <=> 10/5 = 2/5 + b   <=> 10/5 - 2/5 = b  <=> 8/5 = b 

Your equation would be: y = 1/5 x + 8/5

 

If using (-3,1): y = 1/5 x + b would give 1 = 1/5 (-3) + b <=> 5/5 = -3/5 + b   <=> 5/5 + 3/5 = b <=> 8/5 = b
Your equation would also be: y = 1/5 x + 8/5

 

You really don't need to use both points to figure out the equation of the line. I just wanted to show you that they would both give the same answer. 

 

Hope it helped!

 

Laurence