Question

put the following equation of a line into slope-intercept form, simplifying all fractions. 3y - 3x = -27

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. We need to solve the equation \(3y-3x=-27\) for \(y\).
First, add \(3x\) to both sides of the equation:
\(3y-3x + 3x=-27 + 3x\)
Simplifying the left - hand side gives \(3y=3x - 27\).

Step2: Solve for y

Divide every term in the equation \(3y = 3x-27\) by 3:
\(\frac{3y}{3}=\frac{3x}{3}-\frac{27}{3}\)
Simplifying each term, we get \(y=x - 9\).

Answer:

\(y = x-9\)