Given the linear equation;
[tex]13x+4y=52-----1[/tex]We can find the slope by comparing the above equation with the general equation of a line. This can be seen below.
[tex]y=mx+c------2[/tex]Where m is the slope of the equation
We then make y the subject of the formula in equation one
[tex]\begin{gathered} 13x+4y=52 \\ \text{subtract 13x from both sides} \\ 13x-13x+4y=52-13x \\ 4y=52-13x \\ \text{Divide both sides by 4} \\ \frac{4y}{4}=\frac{52}{4}-\frac{13x}{4} \\ y=13-\frac{13x}{4} \end{gathered}[/tex]By comparison,
[tex]m=-\frac{13}{4}[/tex]Answer: The slope of the equation is
[tex]\text{slope}=-\frac{13}{4}[/tex]