To solve the question about finding the slope of the line shown on the graph:

Step 1: Review Slope Formula

The slope ($m$) of a line is given by: $m = \frac{\text{vertical change}}{\text{horizontal change}}$ This is represented by the ratio of "rise" (change in $y$) over "run" (change in $x$), matching option D in the choices provided.

Step 2: Calculate the Slope

To find the slope, pick two points on the line. The graph shows points at:

• $(-10, 8)$
• $(10, -4)$

Calculate the change in $y$ (vertical change) and the change in $x$ (horizontal change):

1. Vertical Change (Change in $y$): $-4 - 8 = -12$
2. Horizontal Change (Change in $x$): $10 - (-10) = 10 + 10 = 20$

So, the slope $m$ is: $m = \frac{-12}{20} = -\frac{3}{5}$

Final Answer

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

Would you like further details or have any questions on this? Here are some related questions to deepen your understanding:

1. What does a negative slope indicate about the direction of a line?
2. How would the slope formula change if we were given different coordinates?
3. How can you verify your answer by choosing other points on the line?
4. How would the slope be affected if the line were vertical or horizontal?
5. What does the absolute value of the slope tell us about the steepness of the line?

Tip: Always simplify fractions when calculating the slope to make sure your answer is in its simplest form.