Given:
Two points are given as (-3,1) and (1,3)
[tex]\begin{gathered} (x_1,y_1)=\left(-3,1\right) \\ (x_2,y_2)=\left(1,3\right) \end{gathered}[/tex]Required:
We want to write an equation which passes through the given points
Explanation:
First we need to find the slope of the required line
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-1}{1-(-3)}=\frac{2}{4}=\frac{1}{2}[/tex]The equation of is
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-1=\frac{x}{2}+\frac{3}{2} \\ \\ y=\frac{x}{2}+\frac{5}{2} \end{gathered}[/tex]Final answer:
[tex]y=\frac{x}{2}+\frac{5}{2}[/tex]