To graph the equation $3x - 2y - 6 = 0$, let's rewrite it in slope-intercept form (i.e., $y = mx + b$), where $m$ is the slope and $b$ is the y-intercept.

Steps:

1. Start with the equation: $3x - 2y - 6 = 0$

2. Solve for $y$: $-2y = -3x + 6$ $y = \frac{3}{2}x - 3$

Now, the equation is in the form $y = \frac{3}{2}x - 3$. The slope is $\frac{3}{2}$ and the y-intercept is $-3$.

Plotting the Graph:

• Y-intercept: The graph crosses the y-axis at $(0, -3)$.
• Slope: The slope $\frac{3}{2}$ means that for every 2 units you move horizontally (to the right), you move 3 units vertically (upwards).

You can plot the point $(0, -3)$, and then use the slope to find another point. Starting from $(0, -3)$, go 2 units to the right and 3 units up to reach the point $(2, 0)$.

Now, draw a straight line through the points $(0, -3)$ and $(2, 0)$. That will be the graph of the equation.

Would you like me to generate the visual graph for you?

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Related Questions:

1. What is the importance of the slope in linear equations?
2. How can we find the x-intercept of this equation?
3. How does changing the slope affect the graph?
4. Can you graph a vertical line from a linear equation?
5. What is the general form of a linear equation?

Tip: Always double-check your calculations when converting an equation to slope-intercept form.