To solve the problem, we need the equation that relates the input (let's call it x) to the output (which is the length, in inches). Assuming that there is a linear relationship between x and the length, we can use the equation of a straight line, which is in the form: y = mx + b, where y represents the length and m and b are constants.
So, for this specific problem, we can start by plugging in two points on the line. Let's choose (x = 0, y = 25) and (x = 10, y = 40), if we assume that the length is 25 inches when the input is 0, and the length is 40 inches when the input is 10.
Using these points, we can find the slope (m) of the line: m = (y2 - y1)/(x2 - x1) = (40 - 25)/(10 - 0) = 15/10 = 3/2.
Now, we can find the equation of the line by using the slope-intercept form of a line, y = mx + b. Plugging in the slope (m = 3/2) and one of the points (0, 25):
25 = (3/2)(0) + b
25 = b
So, the equation of the line is y = (3/2)x + 25.
To find the length when x = 5, we can plug in that value into the equation:
y = (3/2)(5) + 25
y = 15/2 + 25
y = 7.5 + 25
y = 32.5 inches
So, when x = 5, the length would be approximately 32.5 inches.
How would you solve it? Once you do, plug in 5 and see how you would get 32 inches.
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