Answer: 16
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Explanation:
y = f(x) since both y and f(x) are outputs of a function
Pick any two columns to select two points from this table. I'll pick the first two columns.
(x1,y1) = (-5,-7)
(x2,y2) = (3,9)
Find the slope of the line through these points
m = (y2-y1)/(x2-x1)
m = (9-(-7))/(3-(-5))
m = (9+7)/(3+5)
m = 16/8
m = 2 is the slope
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Now turn to point slope form and solve for y
y - y1 = m(x - x1)
y - (-7) = 2(x - (-5))
y + 7 = 2(x + 5)
y + 7 = 2x + 10
y = 2x + 10 - 7
y = 2x + 3
f(x) = 2x + 3
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We can now plug in x = 6.5
f(x) = 2x + 3
f(6.5) = 2(6.5) + 3
f(6.5) = 13 + 3
f(6.5) = 16
