To find the equation of a line in point-slope form, we need to follow these steps:

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 the formula:

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

For the points $(0, 4)$ and $(5, 3)$: $m = \frac{3 - 4}{5 - 0} = \frac{-1}{5} = -\frac{1}{5}$

Step 2: Use the point-slope form equation.

The point-slope form of a line is:

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

Using the point $(5, 3)$ as the primary point and the slope $m = -\frac{1}{5}$:

$y - 3 = -\frac{1}{5}(x - 5)$

Thus, the point-slope form of the equation is:

$y - 3 = -\frac{1}{5}(x - 5)$

Would you like further details or clarification?

Here are 5 questions that build on this topic:

1. How do you convert point-slope form to slope-intercept form?
2. Can you verify the slope using a different pair of points?
3. What happens if you use $(0, 4)$ as the primary point instead?
4. How can you find the y-intercept from this point-slope equation?
5. How does point-slope form differ from the standard form of a linear equation?

Tip: Always double-check the slope calculation to avoid errors when finding the equation of a line.