Respuesta :
The form of the linear equation is
[tex]y=mx+b[/tex]m is the slope that represents the rate of profit per year
b is the y-intercept which represents the initial amount in the year 2010
Since y is the profit in millions
Since x is the number of the year starting from 2010, then
At 2012:
The profit is 4 million dollars, y = 4
The year is 2012, x = 2
Substitute them in the rule above
[tex]\begin{gathered} 4=m(2)+b \\ 4=2m+b \\ 2m+b=4\rightarrow(1) \end{gathered}[/tex]At 2016:
The profit is 13.2 million dollars, y = 13.2
The year is 2016, x = 6
Substitute them in the rule above
[tex]\begin{gathered} 13.2=m(6)+b \\ 13.2=6m+b \\ 6m+b=13.2\rightarrow(2) \end{gathered}[/tex]Now, subtract equation (1) from equation (2) to eliminate b
[tex]\begin{gathered} (6m-2m)+(b-b)=(13.2-4) \\ 4m+0=9.2 \\ 4m=9.2 \end{gathered}[/tex]Divide both sides by 4 to find m
[tex]\begin{gathered} \frac{4m}{4}=\frac{9.2}{4} \\ m=2.3 \end{gathered}[/tex]Substitute m in equation (1) by 2.3
[tex]\begin{gathered} 2(2.3)+b=4 \\ 4.6+b=4 \end{gathered}[/tex]Subtract 4.6 from both sides
[tex]\begin{gathered} 4.6-4.6+b=4-4.6 \\ b=-0.6 \end{gathered}[/tex]m = 2.3 million dollars per year
b = -0.6 million dollar
The equation of the profit is
[tex]\begin{gathered} y=2.3x+(-0.6) \\ y=2.3x-0.6 \end{gathered}[/tex]The answer is
y = 2.3x - 0.6, where y is the profit in million and x is the years since 2010
