To determine the slope of the line given the two points $(0, 4)$ and $(3, -1)$, we use the slope formula:

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

Where:

• $(x_1, y_1) = (0, 4)$
• $(x_2, y_2) = (3, -1)$

Step-by-Step Calculation:

1. Subtract the $y$-coordinates: $y_2 - y_1 = -1 - 4 = -5$

2. Subtract the $x$-coordinates: $x_2 - x_1 = 3 - 0 = 3$

3. Divide the results: $m = \frac{-5}{3}$

Final Answer:

The slope of the line is:

$m = -\frac{5}{3}$

This is already simplified as an improper fraction.

Let me know if you need more explanation or want to explore further examples!

Here are some related questions for practice:

1. What is the slope of a line passing through $(2, 3)$ and $(5, 7)$?
2. How do you interpret a negative slope in the context of a graph?
3. Write the equation of a line with slope $-\frac{5}{3}$ and passing through the point $(0, 4)$.
4. How do you find the slope of a horizontal line?
5. How does the steepness of the line change if the slope is $-\frac{5}{3}$ versus $-2$?

Tip: The slope tells us how steep a line is and its direction: negative slopes go downward from left to right!