SOLUTION: Find a formula for the linear function g(x) where g(5)=75 and g(30)=25

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Question 1025728: Find a formula for the linear function g(x) where g(5)=75 and g(30)=25
Found 2 solutions by Theo, stanbon:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
a linear function will have an equation of y = mx + b

m is the slope
b is the y-intercept.

the slope is equal to the change in y divided by the change in x.

make y = g(x) and you get:

y = 75 when x is 5 and y = 25 when x is 30.

this says that y goes down 50 when x goes up 25.

slope is therefore -50 / 25 = -2.

your general equation of y = mx + b becomes y = 2x + b

replace one of your points with their values and you can solve for b.

when x = 5, y = 75 gets you 75 = -2*5 + b

solve for b to get b = 75 + 10 = 85

your equation becopmes y = -2x + 85

when x = 5, y = -10 + 85 = 75

when x = 30, y = -60 + 85 = 25

looks like the equation is good.

the graph of this equation looks like this:

$$$










Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find a formula for the linear function g(x) where g(5)=75 and g(30)=25
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You have two points:: (5,75) and (30,25)
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slope = m = (25-75)/(30-5) = -50/25 = -2
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Form: y = mx + b
Solve for "b"::
75 = -2*5 + b
b = 85
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Ans: y = 2x+85
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Cheers,
Stan H.
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