SOLUTION: Write an equation in slope-intercept form of the line through (1,3) and (-3,7)

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Question 635639: Write an equation in slope-intercept form of the line through (1,3) and (-3,7)
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=1 and y%5B1%5D=3.
Also, is the second point . So this means that x%5B2%5D=-3 and y%5B2%5D=7.


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


m=%287-3%29%2F%28-3-1%29 Plug in y%5B2%5D=7, y%5B1%5D=3, x%5B2%5D=-3, and x%5B1%5D=1


m=%284%29%2F%28-3-1%29 Subtract 3 from 7 to get 4


m=%284%29%2F%28-4%29 Subtract 1 from -3 to get -4


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-3=-1%28x-1%29 Plug in m=-1, x%5B1%5D=1, and y%5B1%5D=3


y-3=-1x%2B-1%28-1%29 Distribute


y-3=-1x%2B1 Multiply


y=-1x%2B1%2B3 Add 3 to both sides.


y=-1x%2B4 Combine like terms.


y=-x%2B4 Simplify


So the equation that goes through the points and is y=-x%2B4


Notice how the graph of y=-x%2B4 goes through the points and . So this visually verifies our answer.
Graph of y=-x%2B4 through the points and