SOLUTION: Find an expression for the function f(x) whose graph is a line passing through the points (2,5) and (8,1). I know the format is y=mx + b but i forgot how to do it

Algebra ->  Rational-functions -> SOLUTION: Find an expression for the function f(x) whose graph is a line passing through the points (2,5) and (8,1). I know the format is y=mx + b but i forgot how to do it      Log On


   

Question 840457: Find an expression for the function f(x) whose graph is a line passing through the points (2,5) and (8,1).
I know the format is y=mx + b but i forgot how to do it
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (2,5) and (8,1)


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: (x%5B1%5D,y%5B1%5D) is the first point (2,5) and (x%5B2%5D,y%5B2%5D) is the second point (8,1))


m=%281-5%29%2F%288-2%29 Plug in y%5B2%5D=1,y%5B1%5D=5,x%5B2%5D=8,x%5B1%5D=2 (these are the coordinates of given points)


m=+-4%2F6 Subtract the terms in the numerator 1-5 to get -4. Subtract the terms in the denominator 8-2 to get 6




m=-2%2F3 Reduce



So the slope is

m=-2%2F3





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Now let's use the point-slope formula to find the equation of the line:




------Point-Slope Formula------
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and (x%5B1%5D,y%5B1%5D) is one of the given points


So lets use the Point-Slope Formula to find the equation of the line


y-5=%28-2%2F3%29%28x-2%29 Plug in m=-2%2F3, x%5B1%5D=2, and y%5B1%5D=5 (these values are given)



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


y-5=%28-2%2F3%29x%2B4%2F3 Multiply -2%2F3 and -2 to get 4%2F3

y=%28-2%2F3%29x%2B4%2F3%2B5 Add 5 to both sides to isolate y


y=%28-2%2F3%29x%2B19%2F3 Combine like terms 4%2F3 and 5 to get 19%2F3 (note: if you need help with combining fractions, check out this solver)



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Answer:



So the equation of the line which goes through the points (2,5) and (8,1) is:y=%28-2%2F3%29x%2B19%2F3


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-2%2F3 and the y-intercept is b=19%2F3


Notice if we graph the equation y=%28-2%2F3%29x%2B19%2F3 and plot the points (2,5) and (8,1), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%28-2%2F3%29x%2B19%2F3 through the points (2,5) and (8,1)


Notice how the two points lie on the line. This graphically verifies our answer.





So the final answer in function notation is f%28x%29+=+expr%28-2%2F3%29x+%2B+19%2F3