In this image, you are working on a problem related to parallel and perpendicular lines. The given line on the graph appears to have a negative slope, and you are required to find the slopes of the original and perpendicular lines.

Step-by-Step Solution:

1. Determine the slope of the original line:

   • From the graph, we can see that the line is slanting downwards from left to right, which indicates a negative slope.
   • By counting the grid units, the line seems to drop by 1 unit (in the $y$-axis) for every 1 unit it moves horizontally (in the $x$-axis).
   • This suggests that the slope of the original line is $-1$.

2. Calculate the perpendicular slope:

   • The slope of a line perpendicular to another is the negative reciprocal of the original slope.
   • If the original slope is $-1$, the negative reciprocal is: $\text{Perpendicular Slope} = \frac{1}{-1} = 1$

Answer:

• Original Slope: $-1$
• Perpendicular Slope: $1$

These are the values to input in the corresponding boxes for the original slope and the perpendicular slope.

Would you like more details or have any questions about this explanation?

Here are five related questions:

1. How do you find the slope of a line from a graph?
2. What is the relationship between the slopes of parallel lines?
3. How do you calculate the slope of a line given two points?
4. What is the significance of the negative reciprocal when determining perpendicular slopes?
5. Can you have perpendicular lines with undefined slopes?

Tip: Always remember, for perpendicular lines, their slopes multiply to give $-1$, unless one of the lines is vertical.