Calculate the Slope of the Line Passing through B(5,0) and A(0,10)

Calculate the slope of the line that creates a right triangle with the x and y axes and passes through the points $B(5,0),A\lparen0,10)$.

To solve this problem, we'll determine the slope of the line that passes through the points $A(0, 10)$ and $B(5, 0)$. The slope of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:

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

We identify the coordinates of our points:

• $(x_1, y_1) = (5, 0)$
• $(x_2, y_2) = (0, 10)$.

Substitute these coordinates into the slope formula:

$m = \frac{10 - 0}{0 - 5}$.

Simplifying the equation gives:

$m = \frac{10}{-5} = -2$.

Thus, the slope of the line is $-2$.

Therefore, the solution to the problem is $m = -2$.