The form of the linear equation is
[tex]y=mx+b[/tex]
m is the slope of rule
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
b is the y-intercept
Since the line passes through points (1, 2), (-2, 1), then
[tex]\begin{gathered} x_1=-2,y_1=1 \\ x_2=1,y_2=2 \end{gathered}[/tex]
Substitute them in the rule of m to find it
[tex]\begin{gathered} m=\frac{2-1}{1-(-2)} \\ m=\frac{1}{1+2} \\ m=\frac{1}{3} \end{gathered}[/tex]
Substitute it in the form of the equation
[tex]y=\frac{1}{3}x+b[/tex]
To find b substitute x by 1 and y by 2 in the equation
[tex]\begin{gathered} 2=\frac{1}{3}(1)+b \\ 2=\frac{1}{3}+b \end{gathered}[/tex]
Subtract 1/3 from both sides to find b
[tex]\begin{gathered} 2-\frac{1}{3}=\frac{1}{3}-\frac{1}{3}+b \\ \frac{6}{3}-\frac{1}{3}=b \\ \frac{5}{3}=b \end{gathered}[/tex]
The equation of the line is
[tex]y=\frac{1}{3}x+\frac{5}{3}[/tex]
