We have to find the equation of the line going through the two pair of points given.
The equation is:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]The 2 pair of points are:
[tex]\begin{gathered} (x_1,y_1)=(1,-2) \\ \text{and} \\ (x_2,y_2)=(2,2) \end{gathered}[/tex]Now, we just subtitute the coordinates (points) into the respective variables in the equation and do some algebra to get the equation of the line. Shown below:
[tex]\begin{gathered} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ y-(-2)=\frac{2-(-2)}{2-1}(x-1) \\ y+2=\frac{2+2}{1}(x-1) \\ y+2=4(x-1) \\ y+2=4x-4 \\ y=4x-4-2 \\ y=4x-6 \end{gathered}[/tex]