SOLUTION: find the equation of the line with y intercept 2 and point (4,4)

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Question 147311: find the equation of the line with y intercept 2 and point (4,4)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
A line with a y intercept of 2 means that the line goes through the point (0,2)


So let's find the equation of the line through the points (0,2) and (4,4)




First let's find the slope of the line through the points and


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


m=%284-2%29%2F%284-0%29 Plug in y%5B2%5D=4, y%5B1%5D=2, x%5B2%5D=4, x%5B1%5D=0, ,


m=%282%29%2F%284-0%29 Subtract 2 from 4 to get 2


m=%282%29%2F%284%29 Subtract 0 from 4 to get 4


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-0%29 Plug in m=1%2F2, x%5B1%5D=0, and y%5B1%5D=2


y-2=%281%2F2%29x%2B%281%2F2%29%28-0%29 Distribute


y-2=%281%2F2%29x%2B0 Multiply


y=%281%2F2%29x%2B0%2B2 Add 2 to both sides.


y=%281%2F2%29x%2B2 Combine like terms.


y=%281%2F2%29x%2B2 Simplify


So the equation that goes through the points and is y=%281%2F2%29x%2B2


Notice how the graph of y=%281%2F2%29x%2B2 goes through the points and . So this visually verifies our answer.
Graph of y=%281%2F2%29x%2B2 through the points and