The line equation in slope-intercept form is given by
[tex]y=\text{mx}+b[/tex]where m is the slope and b the y-intercept.
From the given points, we can find the slope m as follows,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where
[tex]\begin{gathered} (x_1,y_1)=(-5,-1) \\ (x_2,y_2)=(4,3) \end{gathered}[/tex]Then, by substituting these values into m, we have
[tex]m=\frac{3-(-1)}{4-(-5)}[/tex]which gives
[tex]m=\frac{3+1}{4+5}=\frac{4}{9}[/tex]So, the line has the form
[tex]y=\frac{4}{9}x+b[/tex]In order to find b, we can substitute point (4,3) into the last result. It yields,
[tex]3=\frac{4}{9}(4)+b[/tex]which gives
[tex]\begin{gathered} 3=\frac{16}{9}+b \\ \text{then} \\ b=3-\frac{16}{9} \\ b=\frac{27}{9}-\frac{16}{9} \\ b=\frac{11}{9} \end{gathered}[/tex]Therefore, the answer is:
[tex]y=\frac{4}{9}x+\frac{11}{9}[/tex]