Step 1 is to find the cost function for any length of wire in inches. Refer to the table and you can see that...
110 inches cost $6.60 so the point (x,y) = (110, 6.60) is on the line
125 inches cost $7.50 so the point (x,y) = (125, 7.50) is on the line
We only need two points form this line. Let's find the slope
m = (y2-y1)/(x2-x1)
m = (7.50-6.60)/(125-110)
m = 0.90/15
m = 0.06
The slope is 0.06 meaning that each additional inch costs $0.06 (6 cents) extra.
In other words, the cost is 6 cents per inch.
Plug (x,y) = (110, 6.60) and m = 0.06 into the equation below to solve for b. This will get us the fixed cost
y = mx+b
6.60 = 0.06*110+b
6.60 = 6.60+b
6.60-6.60 = 6.60+b-6.60
0 = b
b = 0
So the fixed cost is 0 which makes sense. If you buy 0 inches of wire (i.e. you don't buy anything) then you don't pay anything.
Therefore the cost function is f(x) = 0.06*x which can be written as y = 0.06*x
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We're told that "Emily needs 23 feet of wire" so we need to convert that feet measurement into inches before we can use the function. The reason why is because x is length in inches (not feet).
23 feet = 23 feet * (12 inches/1 foot) = 23*12 = 276 inches
so in short, 23 feet is equivalent to 276 inches
This means x = 276 and y is...
y = 0.06*x
y = 0.06*276
y = 16.56
Emily will spend 16.56 dollars for her wire.
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Andy needs 14 yards. We'll have to convert from yards to feet
14 yards = 14 yards * (3 feet/1 yard) = 14*3 = 42 feet
14 yards = 42 feet
Then convert that feet measurement to inches
42 feet = 42 feet * (12 inches/1 foot) = 42*12 = 504 inches
So overall,
14 yards = 504 inches
Now we can use the function
y = 0.06*x
y = 0.06*504
y = 30.24
Andy will spend 30.24 dollars for his wire.
Side Note: Andy will spend 13.68 dollars extra compared to Emily (since 30.24-16.56 = 13.68). So Andy spends more. Which makes sense given how Andy needs 504 inches of wire compared to Emily's needs of 276 iches of wire.
