SOLUTION: write the equation in the slope intercept form for the line passing through (2,1) and (-1,3) I know that slope intercept form is y=mx+b and the slope is -2/3 any help?

Algebra ->  Linear-equations -> SOLUTION: write the equation in the slope intercept form for the line passing through (2,1) and (-1,3) I know that slope intercept form is y=mx+b and the slope is -2/3 any help?      Log On


   

Question 147607: write the equation in the slope intercept form for the line passing through (2,1) and (-1,3)
I know that slope intercept form is y=mx+b
and the slope is -2/3
any help?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

First let's find the slope of the line through the points and


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%283-1%29%2F%28-1-2%29 Plug in y%5B2%5D=3, y%5B1%5D=1, x%5B2%5D=-1, x%5B1%5D=2, ,


m=%282%29%2F%28-1-2%29 Subtract 1 from 3 to get 2


m=%282%29%2F%28-3%29 Subtract 2 from -1 to get -3


m=-2%2F3 Reduce


So the slope of the line that goes through the points and is m=-2%2F3


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-1=%28-2%2F3%29%28x-2%29 Plug in m=-2%2F3, x%5B1%5D=2, and y%5B1%5D=1


y-1=%28-2%2F3%29x%2B%28-2%2F3%29%28-2%29 Distribute


y-1=%28-2%2F3%29x%2B4%2F3 Multiply


y=%28-2%2F3%29x%2B4%2F3%2B1 Add 1 to both sides.


y=%28-2%2F3%29x%2B7%2F3 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation that goes through the points and is y=%28-2%2F3%29x%2B7%2F3


Notice how the graph of y=%28-2%2F3%29x%2B7%2F3 goes through the points and . So this visually verifies our answer.
Graph of y=%28-2%2F3%29x%2B7%2F3 through the points and