The line passes through the point:
[tex](-1,-16)\text{ and }(19,11)[/tex]
We can use the slope-intercept form of a linear equation to get the line:
[tex]y=mx+b[/tex]
where
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
The points are:
[tex]\begin{gathered} (x_1,y_1)=(-1,-16) \\ (x_2,y_2)=(19,11) \end{gathered}[/tex]
Using the formula, we have:
[tex]\begin{gathered} m=\frac{11-(-16)}{19-(-1)}=\frac{11+16}{19+1} \\ m=\frac{27}{20} \end{gathered}[/tex]
Thus, the equation is in the form:
[tex]y=\frac{27}{20}x+b[/tex]
At the point (-1, -16), we have:
[tex]\begin{gathered} -16=\frac{27}{20}(-1)+b \\ -16=-\frac{27}{20}+b \\ b=-16+\frac{27}{20} \\ b=-\frac{293}{20} \end{gathered}[/tex]
Therefore, the equation will be:
[tex]y=\frac{27}{20}x-\frac{293}{20}[/tex]
