SOLUTION: Suppose a line goes through the points (3,1) and (-2,-9). Write the equation of the line. Determine the intercepts of the line and sketch the graph.

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Question 902401: Suppose a line goes through the points (3,1) and (-2,-9). Write the equation of the line. Determine the intercepts of the line and sketch the graph.
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=1.
Also, is the second point . So this means that x%5B2%5D=-2 and y%5B2%5D=-9.


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


m=%28-9-1%29%2F%28-2-3%29 Plug in y%5B2%5D=-9, y%5B1%5D=1, x%5B2%5D=-2, and x%5B1%5D=3


m=%28-10%29%2F%28-2-3%29 Subtract 1 from -9 to get -10


m=%28-10%29%2F%28-5%29 Subtract 3 from -2 to get -5


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


y-1=2x%2B2%28-3%29 Distribute


y-1=2x-6 Multiply


y=2x-6%2B1 Add 1 to both sides.


y=2x-5 Combine like terms.


So the equation that goes through the points and is y=2x-5


Notice how the graph of y=2x-5 goes through the points and . So this visually verifies our answer.
Graph of y=2x-5 through the points and

y-intercept is (0,-5)
x-intercept is (2.5, 0)