SOLUTION: What is an equation of the points on the graph(0,5) and (1,1) ?

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Question 202967: What is an equation of the points on the graph(0,5) and (1,1) ?
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=0 and y%5B1%5D=5.
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=%281-5%29%2F%281-0%29 Plug in y%5B2%5D=1, y%5B1%5D=5, x%5B2%5D=1, and x%5B1%5D=0


m=%28-4%29%2F%281-0%29 Subtract 5 from 1 to get -4


m=%28-4%29%2F%281%29 Subtract 0 from 1 to get 1


m=-4 Reduce


So the slope of the line that goes through the points and is m=-4


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-5=-4%28x-0%29 Plug in m=-4, x%5B1%5D=0, and y%5B1%5D=5


y-5=-4x%2B-4%28-0%29 Distribute


y-5=-4x%2B0 Multiply


y=-4x%2B0%2B5 Add 5 to both sides.


y=-4x%2B5 Combine like terms.


y=-4x%2B5 Simplify


So the equation that goes through the points and is y=-4x%2B5


Notice how the graph of y=-4x%2B5 goes through the points and . So this visually verifies our answer.
Graph of y=-4x%2B5 through the points and