SOLUTION: write an equation in slope intercept form of the line passing through each pair of points: (-8,2) and (0,6)

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Question 197548: write an equation in slope intercept form of the line passing through each pair of points: (-8,2) and (0,6)
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=%286-2%29%2F%280--8%29 Plug in y%5B2%5D=6, y%5B1%5D=2, x%5B2%5D=0, and x%5B1%5D=-8


m=%284%29%2F%280--8%29 Subtract 2 from 6 to get 4


m=%284%29%2F%288%29 Subtract -8 from 0 to get 8


m=1%2F2 Reduce


So the slope of the line that goes through the points and is m=1%2F2


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=%281%2F2%29%28x--8%29 Plug in m=1%2F2, x%5B1%5D=-8, and y%5B1%5D=2


y-2=%281%2F2%29%28x%2B8%29 Rewrite x--8 as x%2B8


y-2=%281%2F2%29x%2B%281%2F2%29%288%29 Distribute


y-2=%281%2F2%29x%2B4 Multiply


y=%281%2F2%29x%2B4%2B2 Add 2 to both sides.


y=%281%2F2%29x%2B6 Combine like terms.


y=%281%2F2%29x%2B6 Simplify


So the equation that goes through the points and is y=%281%2F2%29x%2B6


Notice how the graph of y=%281%2F2%29x%2B6 goes through the points and . So this visually verifies our answer.
Graph of y=%281%2F2%29x%2B6 through the points and