Question

What is the slope of the line given by the following equation?  13x + 4y = 52

Answer 1

Given the linear equation;

$13x+4y=52-----1$

We can find the slope by comparing the above equation with the general equation of a line. This can be seen below.

$y=mx+c------2$

Where m is the slope of the equation

We then make y the subject of the formula in equation one

$\begin{gathered} 13x+4y=52 \\ \text{subtract 13x from both sides} \\ 13x-13x+4y=52-13x \\ 4y=52-13x \\ \text{Divide both sides by 4} \\ \frac{4y}{4}=\frac{52}{4}-\frac{13x}{4} \\ y=13-\frac{13x}{4} \end{gathered}$

By comparison,

$m=-\frac{13}{4}$

Answer: The slope of the equation is

$\text{slope}=-\frac{13}{4}$