To write the equation of a line in point-slope form, we need a point on the line and the slope.

Step 1: Find the slope $m$.

The slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Using the points $(2, 0)$ (x-intercept) and $(0, 3)$ (y-intercept):

$m = \frac{3 - 0}{0 - 2} = \frac{3}{-2} = -\frac{3}{2}$

Step 2: Use the point-slope form of the equation.

The point-slope form of a line's equation is:

$y - y_1 = m(x - x_1)$

You can choose either $(2, 0)$ or $(0, 3)$ as the point $(x_1, y_1)$. Using $(2, 0)$:

$y - 0 = -\frac{3}{2}(x - 2)$

This simplifies to:

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

So, the equation of the line in point-slope form is:

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

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How would the equation change if the line had a positive slope?
2. What is the equation of the line in slope-intercept form?
3. Can you find the distance between the x-intercept and y-intercept?
4. How do you convert the equation from point-slope to standard form?
5. What does the slope of $-\frac{3}{2}$ indicate about the direction of the line?

Tip: When working with different forms of a line's equation, remember that converting between them often involves simple algebraic manipulations!