SOLUTION: Find the equation for a line which passes through the points (-3,9) and (1,1). Write the equation in slope-intercept form. Please show work.

Algebra ->  Functions -> SOLUTION: Find the equation for a line which passes through the points (-3,9) and (1,1). Write the equation in slope-intercept form. Please show work.       Log On


   

Question 609962: Find the equation for a line which passes through the points (-3,9) and (1,1). Write the equation in slope-intercept form. Please show work.

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=1.


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


m=%281-9%29%2F%281--3%29 Plug in y%5B2%5D=1, y%5B1%5D=9, x%5B2%5D=1, and x%5B1%5D=-3


m=%28-8%29%2F%281--3%29 Subtract 9 from 1 to get -8


m=%28-8%29%2F%284%29 Subtract -3 from 1 to get 4


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


y-9=-2%28x%2B3%29 Rewrite x--3 as x%2B3


y-9=-2x%2B-2%283%29 Distribute


y-9=-2x-6 Multiply


y=-2x-6%2B9 Add 9 to 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

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