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} \\ (4y)/(4)=(52)/(4)-(13x)/(4) \\ y=13-(13x)/(4) \end{gathered}`

By comparison,

`m=-(13)/(4)`

Answer: The slope of the equation is

`\text{slope}=-(13)/(4)`