The formula for the equation of a line given two points is,
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]Given that
[tex]\begin{gathered} (x_1,y_1)=(1,-2) \\ (x_2,y_2)=(3,2) \end{gathered}[/tex]Substituting the given points to the equation and expressing it in the form, y = mx+b
[tex]\begin{gathered} \frac{y--2}{x-1}=\frac{2--2}{3-1} \\ \frac{y+2}{x-1}=\frac{2+2}{3-1} \\ \frac{y+2}{x-1}=\frac{4}{2} \\ \frac{y+2}{x-1}=2 \end{gathered}[/tex]Cross multiply
[tex]\begin{gathered} y+2=2(x-1) \\ y+2=2x-2 \\ y=2x-2-2 \\ y=2x-4 \\ \therefore y=2x-4 \end{gathered}[/tex]Hence, the equation of a line in slope in y = mx+b is
[tex]y=2x-4[/tex]
