Question

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