SOLUTION: i have to find slope intercept form of the line that passes through (3,5) (0,4)

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Question 674116: i have to find slope intercept form of the line that passes through (3,5) (0,4)
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 . So this means that x%5B1%5D=3 and y%5B1%5D=5.
Also, is the second point . So this means that x%5B2%5D=0 and y%5B2%5D=4.


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


m=%284-5%29%2F%280-3%29 Plug in y%5B2%5D=4, y%5B1%5D=5, x%5B2%5D=0, and x%5B1%5D=3


m=%28-1%29%2F%280-3%29 Subtract 5 from 4 to get -1


m=%28-1%29%2F%28-3%29 Subtract 3 from 0 to get -3


m=1%2F3 Reduce


So the slope of the line that goes through the points and is m=1%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-5=%281%2F3%29%28x-3%29 Plug in m=1%2F3, x%5B1%5D=3, and y%5B1%5D=5


y-5=%281%2F3%29x%2B%281%2F3%29%28-3%29 Distribute


y-5=%281%2F3%29x-1 Multiply


y=%281%2F3%29x-1%2B5 Add 5 to both sides.


y=%281%2F3%29x%2B4 Combine like terms.


So the equation that goes through the points and is y=%281%2F3%29x%2B4


Notice how the graph of y=%281%2F3%29x%2B4 goes through the points and . So this visually verifies our answer.
Graph of y=%281%2F3%29x%2B4 through the points and