Respuesta :
Part 1: Finding slope
Solving the slope requires two points: [tex]$\left(\left(t_{1}, y_{1}\right)\right.$[/tex] and [tex]$\left.\left(t_{2}, y_{2}\right)\right)$[/tex]. The year 1983 corresponds to [tex]$t=3$[/tex] so the first point is (3,33.7). The year 1989 is 6 years after 1983, so the corresponding t value for 1989 should be 6 years after [tex]$t=3$[/tex]; that is, the second point should be (9,47)
Using the slope formula, we determine the slope m:
[tex]m=\frac{\Delta y}{\Delta t}=\frac{y_{2}-y_{1}}{t_{2}-t_{1}}=\frac{47 \mathrm{lb}-33.7 \mathrm{lb}}{9 \mathrm{yr}-3 \mathrm{yr}}=\frac{13.3}{6} \approx 2.22 \mathrm{lb} / \mathrm{yr}[/tex]
Part 2: Finding y-intercept
By plugging the initial point (3,33.7) into the equation, we can compute the y-intercept b of our linear model [tex]$y=2.22 t+b$[/tex] :
[tex]$33.7 \mathrm{lb}=(2.22 \mathrm{lb} / \mathrm{yr})(3 \mathrm{yr})+b$[/tex]
[tex]$b=33.7 \mathrm{lb}-(2.22 \mathrm{lb} / \mathrm{yr})(3 \mathrm{yr})=27.04 \mathrm{lb}$[/tex]
Part 3: Conclusion
The whole linear model explaining per capita consumption in the United States is as follows:
[tex]$y=(2.22 \mathrm{lb} / \mathrm{yr}) t+27.04 \mathrm{lb}$[/tex]
Learn more about slope and y-intercept https://brainly.com/question/4015585
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