SOLUTION: Write an equation of the line the passes through (-5,8) and (-3,-8)

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Question 451296: Write an equation of the line the passes through (-5,8) and (-3,-8)
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=-5 and y%5B1%5D=8.
Also, is the second point . So this means that x%5B2%5D=-3 and y%5B2%5D=-8.


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


m=%28-8-8%29%2F%28-3--5%29 Plug in y%5B2%5D=-8, y%5B1%5D=8, x%5B2%5D=-3, and x%5B1%5D=-5


m=%28-16%29%2F%28-3--5%29 Subtract 8 from -8 to get -16


m=%28-16%29%2F%282%29 Subtract -5 from -3 to get 2


m=-8 Reduce


So the slope of the line that goes through the points and is m=-8


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


y-8=-8%28x%2B5%29 Rewrite x--5 as x%2B5


y-8=-8x%2B-8%285%29 Distribute


y-8=-8x-40 Multiply


y=-8x-40%2B8 Add 8 to both sides.


y=-8x-32 Combine like terms.


y=-8x-32 Simplify


So the equation that goes through the points and is y=-8x-32


Notice how the graph of y=-8x-32 goes through the points and . So this visually verifies our answer.
Graph of y=-8x-32 through the points and