Let's analyze the given linear equation:

$3x - 2y = 6$

Step 1: Rearrange to slope-intercept form ($y = mx + b$):

Start by solving for $y$:

$3x - 2y = 6$ Subtract $3x$ from both sides: $-2y = -3x + 6$ Now divide by $-2$ to isolate $y$: $y = \frac{3}{2}x - 3$

Step 2: Identify the slope and y-intercept:

• Slope (m): $\frac{3}{2}$
• Y-intercept (b): $-3$

Step 3: Plot the graph:

• The line crosses the y-axis at $(0, -3)$.
• Use the slope $\frac{3}{2}$, which means for every 2 units to the right, move 3 units up.

Step 4: Match with the options:

Looking at the options in the image:

• Option D shows the correct line with a positive slope and a y-intercept at $-3$.

Thus, the correct answer is Option D.

Would you like further details on how to graph it manually or any other related questions?

Relative questions:

1. What is the importance of slope-intercept form in graphing linear equations?
2. How do you find the x-intercept of a line given in standard form?
3. Can every linear equation be written in slope-intercept form?
4. How would the graph of the equation change if the slope were negative?
5. How do you graph a line if it's given in point-slope form?

Tip:

Always verify the slope and intercept visually when matching graphs to equations.