SOLUTION: My problem is to write an equation using slope intercept form if possible for (2,-1) and (0,3). I am lost. Please help. Thanks Heather

Algebra ->  Linear-equations -> SOLUTION: My problem is to write an equation using slope intercept form if possible for (2,-1) and (0,3). I am lost. Please help. Thanks Heather      Log On


   

Question 307211: My problem is to write an equation using slope intercept form if possible for (2,-1) and (0,3). I am lost. Please help. Thanks Heather
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


Note: is the first point . So this means that x%5B1%5D=2 and y%5B1%5D=-1.
Also, is the second point . So this means that x%5B2%5D=0 and y%5B2%5D=3.


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%280-2%29 Plug in y%5B2%5D=3, y%5B1%5D=-1, x%5B2%5D=0, and x%5B1%5D=2


m=%284%29%2F%280-2%29 Subtract -1 from 3 to get 4


m=%284%29%2F%28-2%29 Subtract 2 from 0 to get -2


m=-2 Reduce


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


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


y%2B1=-2%28x-2%29 Rewrite y--1 as y%2B1


y%2B1=-2x%2B-2%28-2%29 Distribute


y%2B1=-2x%2B4 Multiply


y=-2x%2B4-1 Subtract 1 from both sides.


y=-2x%2B3 Combine like terms.


So the equation that goes through the points and is y=-2x%2B3


Notice how the graph of y=-2x%2B3 goes through the points and . So this visually verifies our answer.
Graph of y=-2x%2B3 through the points and