Since a single line passes through two points, then you can first obtain the slope of the line using the formula
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where m is the slope and the line and} \\ (x_1,y_1),(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}[/tex]
And then use the point-slope formula to find the equation of the line, that is
[tex]y-y_1=m(x-x_1)[/tex]
So, in this case, you have
[tex]\begin{gathered} (x_1,y_1)=(-2,4) \\ (x_2,y_2)=(1,13) \end{gathered}[/tex][tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=\frac{13-4}{1-(-2)} \\ m=\frac{9}{1+2} \\ m=\frac{9}{3} \\ m=3 \end{gathered}[/tex]
Now, using the point-slope formula
[tex]\begin{gathered} y-4=3(x-(-2)) \\ y-4=3(x+2) \end{gathered}[/tex]
Therefore, the correct answer is A.
[tex]y-4=3(x+2)[/tex]
