SOLUTION: The following are a set of points, where there is one unknown value. Use linear interpolation to determine the unknown value, y. Provide your answer to two decimal places. (x0,y0)

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Question 1160199: The following are a set of points, where there is one unknown value. Use linear interpolation to determine the unknown value, y. Provide your answer to two decimal places. (x0,y0)=(10,80), (x1,y1)=(40,5), (x,y)=(x,43.85)
Found 2 solutions by MathLover1, Alan3354:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The following are a set of points, where there is one unknown value. Use linear interpolation to determine the unknown value, y. Provide your answer to two decimal places.
(x%5B0%5D,y%5B0%5D)=(10,80)
(x%5B1%5D,y%5B1%5D)=(40,5)
(x,y)=(x,43.85)
all points lie on same line
find equation of the line using two of the given points
The equation of a line is typically written as y=mx%2Bbwhere m is the slope and b is the y-intercept.
first use points to find the slope m
m=%28y%5B1%5D-y%5B0%5D%29%2F%28x%5B1%5D-x%5B0%5D%29
m=%285-80%29%2F%2840-10%29
m=-75%2F30
m=-5%2F2
so far your equation is:
y=-%285%2F2%29x%2Bb.........use one point to calculate b
5=-%285%2F2%2940%2Bb
5=-5%2A20%2Bb
5=-100%2Bb
b=5%2B100
b=105

your equation is:
y=-%285%2F2%29x%2B105
now calculate missing coordinate (x,43.85)
43.85=-%285%2F2%29x%2B105
43.85-105=-%285%2F2%29x
-61.15=-%285%2F2%29x
x=-61.15%2F%28-5%2F2%29
x=24.46

answer:
(24.46,43.85)






Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The following are a set of points, where there is one unknown value. Use linear interpolation to determine the unknown value, y. Provide your answer to two decimal places. (x0,y0)=(10,80), (x1,y1)=(40,5), (x,y)=(x,43.85)
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Tho the instruction to use linear interpolation implies that it's a straight line, it should be specified.