Which number line shows the correct way to find the sum p+q if p is positive and q is negative?(1 point)

Question

Responses

Image with alt text: A number line is shown with arrows at both ends, and hashmarks at unit intervals. The second mark from the left is labeled 0. Point p is located 5 intervals to the right of 0. A leftward curved arrow, labeled absolute value of q, starts at p and ends 4 intervals to the left of p.

Image with alt text: A number line is shown with arrows at both ends, and hashmarks at unit intervals. The second point from the left is labeled p. Zero is marked at 6 intervals to the right of point p. A rightward curved arrow, labeled absolute value of q, starts at p and ends 4 intervals to the right of p.

Image with alt text: A number line is shown with arrows at both ends, and hashmarks at unit intervals. Point p is marked on the seventh interval from the left. Zero is marked 2 intervals to the right of p. A leftward curved arrow, labeled absolute value of q, points from p to the second interval from the left.

Answer 1

To find the sum $p+q$ when $p$ is positive and $q$ is negative, we need to start from point $p$ and move left on the number line by the absolute value of $q$ (since $q$ is negative).

Let's analyze the descriptions of the number lines you provided:

1. First image: Shows $p$ at 5 intervals to the right of 0. A leftward arrow labeled $|q|$ (the absolute value of $q$) starts at $p$ and ends 4 intervals to the left of $p$. This is correct because it indicates moving left from $p$ by the positive distance $|q|=4$, representing the addition of a negative number to a positive one.

2. Second image: Begins at $p$ and incorrectly moves right by $|q|$ (which would imply adding a positive number instead of subtracting). This does not reflect the operation of adding a negative.

3. Third image: Shows $p$ at the seventh interval from the left, with zero marked at 2 intervals to the right of $p$. An arrow moves left to the second interval from the left, indicating that $q$ has a value that brings us back by the absolute value of $q$. This method reflects the correct representation of adding a negative number.

Based on these descriptions, the correct number line for the operation $p+q$ is displayed in the first image, as it correctly illustrates moving left from $p$ to find the sum.