To calculate the slope of the line shown in the image, we use the slope formula:

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

Here, the two points given are $(0, 4)$ and $(3, -1)$.

Step 1: Assign coordinates

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

Step 2: Substitute into the formula

$m = \frac{-1 - 4}{3 - 0} = \frac{-5}{3}$

Step 3: Simplify

The slope of the line is:

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

Final Answer:

The slope of the line is $-\frac{5}{3}$.

Do you need further explanation or details on the steps? Let me know!

Related Questions:

1. What is the equation of the line in slope-intercept form using the given slope?
2. How do you interpret the meaning of a negative slope?
3. Can you find another point on the line using the slope?
4. What is the slope of a line perpendicular to this one?
5. How would the slope change if one of the points were adjusted?

Tip:

Always double-check that the coordinates are substituted correctly into the slope formula to avoid small errors.