To convert the equation $9y - 3x = -54$ into slope-intercept form, we need to isolate $y$ on one side of the equation in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Steps:

1. Add $3x$ to both sides: $9y = 3x - 54$

2. Divide every term by 9 to solve for $y$: $y = \frac{3x}{9} - \frac{54}{9}$

3. Simplify the equation: $y = \frac{1}{3}x - 6$

Slope-Intercept Form:

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

• Slope ($m$): $\frac{1}{3}$
• Y-intercept ($b$): $-6$

Would you like further details on this, or do you have any other questions?

Here are 5 related questions for practice:

1. How do you find the slope from the standard form of an equation?
2. What is the slope-intercept form of the equation $4x - 2y = 8$?
3. How do you determine the x-intercept from a slope-intercept form equation?
4. If you know the slope and a point on the line, how can you write the equation?
5. How does changing the slope $m$ affect the line on a graph?

Tip: Always check the equation after isolating $y$ to ensure the form matches $y = mx + b$.