Answer:
[tex]y=\frac{5}{4}x-3[/tex]Step-by-step explanation:
Linear functions are represented by the following equation:
[tex]\begin{gathered} y=mx+b \\ \text{where,} \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}[/tex]The slope of a line is given as;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex](-4,-8) and (-8,-13):
[tex]\begin{gathered} m=\frac{-8-(-13)}{-4-(-8)} \\ m=\frac{5}{4} \end{gathered}[/tex]Use the slope-point form of a line, to find the slope-intercept form:
[tex]\begin{gathered} y_{}-y_1=m(x_1-x_{}) \\ y+8=\frac{5}{4}(x+4) \\ y+8=1.25\mleft(x+4\mright) \\ y=\frac{5}{4}x-13 \\ y+8=\frac{5}{4}x+\frac{20}{4} \\ y=\frac{5}{4}x+5-8 \\ y=\frac{5}{4}x-3 \end{gathered}[/tex]