The equation for a straight line (deterministic model) is y = Bo + B,X.If the line passes through the point ( - 10,3), then x = - 10, y = 3 must satisfy the equation; that is, 3 = Bo + B1(-10).Similarly, if the line passes through the point (11,4), then x = 11, y = 4 must satisfy the equation; that is, 4 = Bo+B1(11).Use these two equations to solve for Bo and By; then find the equation of the line that passes through the points (-10,3) and (11,4)...Find Bo and B,B1 =Bo(Simplify your answers. Type integers or simplified fractions.)

To find the equation of the line we just need to find the beta constants. In order to do this we have (they provided us with) the following system of equations:

[tex]\begin{cases}3=\beta_0+\beta_1(-10) \\ 4=\beta_0+\beta_1(11)\end{cases}[/tex]

Let us subtract the second equation to the first one:

This implies that

[tex]\beta_1=\frac{-1}{-21}=\frac{1}{21}[/tex]

Now, let us replace this value we just got into the second equation to find beta_0:

[tex]\begin{gathered} 4=\beta_0+\frac{1}{21}\cdot11, \\ 4=\beta_0+\frac{11}{21}, \\ \beta_0=4-\frac{11}{21}=\frac{4\cdot21}{21}-\frac{11}{21}=\frac{84-11}{21}=\frac{73}{21} \end{gathered}[/tex]

At last,

[tex]\beta_1=\frac{1}{21},\beta_0=\frac{73}{21}[/tex]

Then, the equation of the line is just

[tex]y=\frac{73}{21}+\frac{1}{21}x[/tex]