From the image, there are two lines on the graph, and you are tasked with identifying the original slope and the perpendicular slope.

Step 1: Identify the slope of the original line

The slope of a line is determined using the formula:

$m = \frac{\text{rise}}{\text{run}}$

Observing the green line:

The green line passes through two points:

• $(0, 5)$ (y-intercept)
• $(3, -4)$

The slope can be calculated as:

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4 - 5}{3 - 0} = \frac{-9}{3} = -3$

Thus, the original slope is -3.

Step 2: Find the perpendicular slope

The slope of a line perpendicular to another is the negative reciprocal of the original slope. The negative reciprocal of $-3$ is:

$\text{Perpendicular slope} = \frac{1}{3}$

Final Answer:

• Original Slope: $-3$
• Perpendicular Slope: $\frac{1}{3}$

Let me know if you need any clarifications or more detailed steps!

Related Questions:

1. How do you calculate the slope between two points?
2. What is the slope of a horizontal line? What about a vertical line?
3. How do you determine if two lines are perpendicular using slopes?
4. What is the equation of the green line in slope-intercept form ($y = mx + b$)?
5. Can you determine the y-intercept of the perpendicular line passing through a point?

Tip:

When finding perpendicular slopes, remember: multiply the original slope by its negative reciprocal to get $-1$.