To solve these questions, let's analyze each one step-by-step:

(a) Which is a point 7 units to the left of 1?

Moving 7 units to the left on a number line means subtracting 7 from the point at 1. Mathematically, we calculate this as: $1 + (-7) = 1 - 7 = -6$ The correct answer for part (a) is: $1 + (-7)$.

(b) Which is a point 7 units to the right of 1?

Moving 7 units to the right on a number line means adding 7 to the point at 1. Mathematically, we calculate this as: $1 + 7 = 8$ The correct answer for part (b) is: $1 + 7$.

Would you like more details on this solution, or do you have any further questions?

Here are some related questions to explore:

1. What happens if we move to the left or right of negative numbers on the number line?
2. How can we visualize addition and subtraction on a number line with larger numbers?
3. What does it mean to move a certain number of units in a specific direction from zero?
4. How would the answers change if we started from a different point, such as -5?
5. Can we represent multiplication as movements on a number line?

Tip: When working with number lines, moving to the left means subtracting, while moving to the right means adding.