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Question 1190061: Decide which of the two given functions is linear and find its equation.
x 0 1 2 3 4
f(x) 7 9 11 13 15
g(x) 9 9 13 11 15
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
f(x) is linear because each time x goes up by 1, the y = f(x) value goes up by 2.
slope = rise/run
slope = (change in y)/(change in x)
slope = 2/1
slope = 2
For g(x), the gap between adjacent values isn't the same, so g(x) isn't linear.
Back to f(x), we have a slope of m = 2 and y intercept b = 7 due to the point (x,y) = (0,7)
The equation y = mx+b becomes y = 2x+7
Therefore, f(x) = 2x+7 is linear.
You can verify that equation by plugging in various values of x to get corresponding y = f(x) values.
For instance, if x = 4, then,
f(x) = 2x+7
f(4) = 2(4)+7
f(4) = 8+7
f(4) = 15
This matches with the last column.
I'll let you check the others.
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