Calculate the Slope of the Line Formed by Points (0,0) and (5,-2): An Analytical Approach

A straight line is drawn between the y axis and the straight line $y=-2$ to create a triangle.

The line passes through the points $B(5,-2),A\lparen0,0)$.

Calculate the slope of the line.

To solve this problem, we'll calculate the slope using the slope formula:

• Step 1: Identify the coordinates of the points. We have point $A(0, 0)$ and point $B(5, -2)$.
• Step 2: Apply the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$.
• Step 3: Substitute the coordinates: $(x_1, y_1) = (0, 0)$ and $(x_2, y_2) = (5, -2)$.

Now, let's work through each step:

The slope formula is:
$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 0}{5 - 0}$.

This simplifies to:
$m = \frac{-2}{5}$.

Therefore, the solution to the problem is $m = -\frac{2}{5}$.

The correct answer choice is $-\frac{2}{5}$.