To find the slope of a line perpendicular to the given line, we need to first determine the slope of the given line.

Step 1: Convert the equation to slope-intercept form

The given equation is:

$2x + 3y = -3$

We need to rearrange this into the slope-intercept form, $y = mx + b$, where $m$ represents the slope.

1. Subtract $2x$ from both sides:

$3y = -2x - 3$

2. Divide both sides by 3 to solve for $y$:

$y = \frac{-2x - 3}{3}$

This simplifies to:

$y = -\frac{2}{3}x - 1$

Step 2: Identify the slope of the given line

From the equation $y = -\frac{2}{3}x - 1$, we can see that the slope of the given line is $m = -\frac{2}{3}$.

Step 3: Find the slope of the perpendicular line

The slopes of two perpendicular lines are negative reciprocals of each other. So, to find the slope of a line perpendicular to the given one, we take the negative reciprocal of $-\frac{2}{3}$:

$\text{Perpendicular slope} = \frac{3}{2}$

Final Answer:

The slope of a line perpendicular to the given line is:

$\boxed{\frac{3}{2}}$

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Would you like further explanation or details? Here are some related questions for you:

1. How do you find the slope of a line from its equation in standard form?
2. What is the condition for two lines to be perpendicular?
3. How do you graph a line given its slope and y-intercept?
4. How do you find the equation of a line perpendicular to a given line passing through a specific point?
5. What happens if two lines have the same slope?

Tip: To quickly check if two lines are perpendicular, multiply their slopes. If the product is $-1$, the lines are perpendicular.