Answer:
36.5 inches
Step-by-step explanation:
Given
See attachment for the given data
Required
Which length is closest to 4.2lb
The given data is a linear dataset.
So, we start by calculating the slope (m)
[tex]m =\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Pick any two corresponding points from the table
So, we have:
[tex](x_1,y_1) = (8,1.21)[/tex]
[tex](x_2,y_2) = (12,1.63)[/tex]
So:
[tex]m =\frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m =\frac{1.63 - 1.21}{12 - 8}[/tex]
[tex]m =\frac{0.42}{4}[/tex]
[tex]m =0.105[/tex]
The linear equation is then calculated using:
[tex]y = m(x - x_1) + y_1[/tex]
This gives:
[tex]y = 0.105 * (x - 8) + 1.21[/tex]
Open bracket
[tex]y = 0.105x - 0.84 + 1.21[/tex]
[tex]y = 0.105x + 0.37[/tex]
To get the length closest to 4.2lb,
we set [tex]y = 4.2[/tex]
Then solve for x
So, we have:
[tex]y = 0.105x + 0.37[/tex]
[tex]4.2 = 0.105x + 0.37[/tex]
Collect like terms
[tex]0.105x= 4.2 - 0.37[/tex]
[tex]0.105x= 3.83[/tex]
Solve for x
[tex]x= 3.83/0.105[/tex]
[tex]x\approx 36.5[/tex]
