Answer :
Given the points (2,-1) and (1,3), we find the slope of the line that passes through them with the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Then, in this case we have:
[tex]\begin{gathered} (x_1,y_1)=(2,-1) \\ (x_2,y_2)=(1,3) \\ \Rightarrow m=\frac{3-(-1)}{1-2}=\frac{3+1}{-1}=\frac{4}{-1}=-4 \\ m=-4 \end{gathered}[/tex]We have that the slope is -4. Now we use the first point to write the equation of the line in point-slope form:
[tex]\begin{gathered} (x_1,y_1)=(2,-1) \\ m=-4 \\ y-y_1=m\cdot(x-x_1) \\ \Rightarrow y-(-1)=-4\cdot(x-2) \\ y+1=-4\cdot(x-2) \end{gathered}[/tex]therefore, the equation in point-slope form is y+1=-4(x-2)