SOLUTION: Write a slope-intercept equation for a line that passes through (3,-9) and (-1,3).

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Question 473562: Write a slope-intercept equation for a line that passes through (3,-9) and (-1,3).
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=3 and y%5B1%5D=-9.
Also, is the second point . So this means that x%5B2%5D=-1 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--9%29%2F%28-1-3%29 Plug in y%5B2%5D=3, y%5B1%5D=-9, x%5B2%5D=-1, and x%5B1%5D=3


m=%2812%29%2F%28-1-3%29 Subtract -9 from 3 to get 12


m=%2812%29%2F%28-4%29 Subtract 3 from -1 to get -4


m=-3 Reduce


So the slope of the line that goes through the points and is m=-3


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--9=-3%28x-3%29 Plug in m=-3, x%5B1%5D=3, and y%5B1%5D=-9


y%2B9=-3%28x-3%29 Rewrite y--9 as y%2B9


y%2B9=-3x%2B-3%28-3%29 Distribute


y%2B9=-3x%2B9 Multiply


y=-3x%2B9-9 Subtract 9 from both sides.


y=-3x%2B0 Combine like terms.


y=-3x Remove the trailing zero


y=-3x Simplify


So the equation that goes through the points and is y=-3x


Notice how the graph of y=-3x goes through the points and . So this visually verifies our answer.
Graph of y=-3x through the points and