Question

question
put the following equation of a line into slope - intercept form, simplifying all fractions.
3y - 2x = -9

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 given equation \(3y-2x=-9\) for \(y\).

Step2: Isolate the term with \(y\)

First, add \(2x\) to both sides of the equation:
\(3y-2x + 2x=-9 + 2x\)
Simplifying the left - hand side, we get \(3y=2x-9\)

Step3: Solve for \(y\)

Divide each term in the equation \(3y = 2x-9\) by \(3\):
\(y=\frac{2x}{3}-\frac{9}{3}\)

Step4: Simplify the fractions

Simplify \(\frac{9}{3}\) to \(3\). So the equation becomes \(y=\frac{2}{3}x-3\)

Answer:

\(y = \frac{2}{3}x-3\)