SOLUTION: Find the slope of the graph of the linear function f f(5/2) = 7/2 f(4) = 6 I am a parent trying to answer my sons question and explain it to him Thanks

Algebra ->  Linear-equations -> SOLUTION: Find the slope of the graph of the linear function f f(5/2) = 7/2 f(4) = 6 I am a parent trying to answer my sons question and explain it to him Thanks      Log On


   

Question 243546: Find the slope of the graph of the linear function f
f(5/2) = 7/2
f(4) = 6
I am a parent trying to answer my sons question and explain it to him
Thanks
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: f(x) is used in place of y. So this means that the line goes through the two points (5/2,7/2) and (4,6)


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%2F2 and y%5B1%5D=7%2F2.
Also, is the second point . So this means that x%5B2%5D=4 and y%5B2%5D=6.


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


m=%286-7%2F2%29%2F%284-5%2F2%29 Plug in y%5B2%5D=6, y%5B1%5D=7%2F2, x%5B2%5D=4, and x%5B1%5D=5%2F2


m=%285%2F2%29%2F%284-5%2F2%29 Subtract 7%2F2 from 6 to get 5%2F2


m=%285%2F2%29%2F%283%2F2%29 Subtract 5%2F2 from 4 to get 3%2F2


m=%285%2F2%29%2A%282%2F3%29 Multiply the first fraction by the reciprocal of the second fraction.


m=5%2F3 Multiply and reduce.


So the slope of the line that goes through the points and is m=5%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-7%2F2=%285%2F3%29%28x-5%2F2%29 Plug in m=5%2F3, x%5B1%5D=5%2F2, and y%5B1%5D=7%2F2


y-7%2F2=%285%2F3%29x%2B%285%2F3%29%28-5%2F2%29 Distribute


y-7%2F2=%285%2F3%29x-25%2F6 Multiply


y=%285%2F3%29x-25%2F6%2B7%2F2 Add 7%2F2 to both sides.


y=%285%2F3%29x-2%2F3 Combine like terms.


y=%285%2F3%29x-2%2F3 Simplify


So the equation that goes through the points and is y=%285%2F3%29x-2%2F3


Notice how the graph of y=%285%2F3%29x-2%2F3 goes through the points and . So this visually verifies our answer.

Graph of y=%285%2F3%29x-2%2F3 through the points and

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the slope of the graph of the linear function f
f(5/2) = 7/2
f(4) = 6
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You have been given two points: (5/2,7/2) and (4,6)
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These points are in the form (x,y)
-------------------------
the slope = (change in the y values)/(change in the x values)
---
slope = [6 - (7/2))/(4 - (5/2))
slope = [(12/2) - (7/2)] / [(8/2)- (5/2)]
slope = (5/2)/(3/2)
Invert the denominator and multipl to get:
slope = (5/2)(2/3)
Cancel the 2 that is in the numerator and in the denominator to get:
slope = 5/3
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Cheers,
Stan H.