To determine the slope of the line that contains two points $A(0,5)$ and $B(5,0)$, we can use the slope formula:

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

Where:

• $(x_1, y_1)$ are the coordinates of point $A$
• $(x_2, y_2)$ are the coordinates of point $B$

Using the given points:

• $A(0,5)$, so $x_1 = 0$, $y_1 = 5$
• $B(5,0)$, so $x_2 = 5$, $y_2 = 0$

Substitute these values into the slope formula:

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

Thus, the slope of the line is:

$m = -1$

Would you like further details or explanations?

Here are 5 related questions to expand your understanding:

1. What is the slope of a vertical line?
2. How do you find the equation of a line given two points?
3. What does a slope of -1 mean geometrically?
4. Can the slope of a line be zero, and what does that indicate?
5. How would you calculate the slope if one point lies on the origin?

Tip: The slope tells us how steep a line is; a negative slope indicates the line is sloping downward from left to right.