SOLUTION: write an equation in slope intercept form of the line passing through each pair of points: (6,-2) and (3,-4)

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Question 197547: write an equation in slope intercept form of the line passing through each pair of points: (6,-2) 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 and is the second point .


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


m=%28-4--2%29%2F%283-6%29 Plug in y%5B2%5D=-4, y%5B1%5D=-2, x%5B2%5D=3, and x%5B1%5D=6


m=%28-2%29%2F%283-6%29 Subtract -2 from -4 to get -2


m=%28-2%29%2F%28-3%29 Subtract 6 from 3 to get -3


m=2%2F3 Reduce


So the slope of the line that goes through the points and is m=2%2F3


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--2=%282%2F3%29%28x-6%29 Plug in m=2%2F3, x%5B1%5D=6, and y%5B1%5D=-2


y%2B2=%282%2F3%29%28x-6%29 Rewrite y--2 as y%2B2


y%2B2=%282%2F3%29x%2B%282%2F3%29%28-6%29 Distribute


y%2B2=%282%2F3%29x-4 Multiply


y=%282%2F3%29x-4-2 Subtract 2 from both sides.


y=%282%2F3%29x-6 Combine like terms.


So the equation that goes through the points and is y=%282%2F3%29x-6


Notice how the graph of y=%282%2F3%29x-6 goes through the points and . So this visually verifies our answer.
Graph of y=%282%2F3%29x-6 through the points and