To find the linear equation that passes through two given points, we forst need to calculate the slope using the following formula:
[tex]\begin{gathered} m=\frac{rise}{run} \\ \\ m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex]
So, the slope of the line that passes through (1, -3) and (3, 9) is:
[tex]\begin{gathered} m=\frac{9-(-3)}{3-1} \\ \\ m=\frac{12}{2} \\ \\ m=6 \end{gathered}[/tex]
Using the point-slope form, the equation of the line is:
[tex]\begin{gathered} (y-y_1)=m(x-x_1) \\ \\ (y+3)=6(x-1) \\ \\ or \\ \\ (y-9)=6(x-3) \end{gathered}[/tex]
The answers are options A and B.
