To first answer this question, we need to find the slope of the linear equation. We have the following information:
x1 = 1960, y1 = 3.91
x2 = 1980, y2 = 3.81
Then
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3.81-3.91}{1980-1960}=-0.005[/tex]Then, we have that the linear model will be:
[tex]y-y1=m\cdot(x-x1)\Rightarrow y-3.91=-0.005\cdot(x-1960)_{}[/tex]Or
[tex]y=-0.005\cdot(x-1960)+3.91\Rightarrow y=-0.005x+13.71[/tex]This is the linear model.
Then, to use the model to estimate the record time in 2000 and in 2020, we have:
[tex]y=-0.005\cdot(2000)+13.71\Rightarrow y=3.71[/tex]And
[tex]y=-0.005\cdot(2020)+13.71\Rightarrow y=3.61[/tex]Therefore, the linear model is y = -0.005x + 13.71.
The estimation for the record time in 2000 is 3.71 minutes.
The estimation for the record time in 2020 is 3.61 minutes.
This is a linear model.
