Question

put the following equation of a line into slope-intercept form, simplifying all fractions. 3x + 15y = -60

Explanation:

Step1: Isolate the y - term

We start with the equation \(3x + 15y=- 60\). First, we want to get the term with \(y\) by itself on one side of the equation. So we subtract \(3x\) from both sides of the equation.
\(15y=-3x - 60\)

Step2: Solve for y

Now, we divide every term in the equation by \(15\) to solve for \(y\). The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.
Dividing each term: \(y=\frac{-3x}{15}+\frac{-60}{15}\)
Simplify the fractions: \(\frac{-3x}{15}=-\frac{1}{5}x\) and \(\frac{-60}{15}=- 4\)
So \(y =-\frac{1}{5}x-4\)

Answer:

\(y =-\frac{1}{5}x - 4\)