SOLUTION: Find the slope-intercept form of the line that passes through the points (2,-1)and (-3,4).

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Question 538943: Find the slope-intercept form of the line that passes through the points (2,-1)and (-3,4).
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=-3 and y%5B2%5D=4.


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


m=%284--1%29%2F%28-3-2%29 Plug in y%5B2%5D=4, y%5B1%5D=-1, x%5B2%5D=-3, and x%5B1%5D=2


m=%285%29%2F%28-3-2%29 Subtract -1 from 4 to get 5


m=%285%29%2F%28-5%29 Subtract 2 from -3 to get -5


m=-1 Reduce


So the slope of the line that goes through the points and is m=-1


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


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


y%2B1=-1x%2B-1%28-2%29 Distribute


y%2B1=-1x%2B2 Multiply


y=-1x%2B2-1 Subtract 1 from both sides.


y=-1x%2B1 Combine like terms.


y=-x%2B1 Simplify


So the equation that goes through the points and is y=-x%2B1


Notice how the graph of y=-x%2B1 goes through the points and . So this visually verifies our answer.
Graph of y=-x%2B1 through the points and


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Jim