Question

question
ut the following equation of a line into slope-intercept form, simplifying all fractions
9y - 3x = -54
answer attempt 1 out of 2

Explanation:

Step1: Isolate the y-term

We start with the equation \(9y - 3x = -54\). First, we add \(3x\) to both sides of the equation to get the \(y\)-term by itself on the left side.

$$9y-3x + 3x=-54 + 3x$$

Simplifying the left side (the \(-3x\) and \(+3x\) cancel out) and the right side, we have:

$$9y=3x - 54$$

Step2: Solve for y

Now, we divide every term in the equation by \(9\) to solve for \(y\).
For the left side: \(\frac{9y}{9}=y\)
For the right side: \(\frac{3x}{9}-\frac{54}{9}\)
Simplify the fractions: \(\frac{3x}{9}=\frac{1}{3}x\) (since \(3\div3 = 1\) and \(9\div3=3\)) and \(\frac{54}{9} = 6\) (since \(54\div9 = 6\))
So we get:

$$y=\frac{1}{3}x-6$$

Answer:

\(y=\frac{1}{3}x - 6\)