Find the Value at the Red Point: Number Line Coordinate Mapping

Q: How do I find the interval between points on a number line?

Look at two consecutive labeled points and subtract the smaller from the larger. For example: $ -1.5 - (-3) = -1.5 + 3 = 1.5 $

Q: What if the red point is between two unlabeled points?

First establish the pattern using labeled points, then extend it step by step. Each tick mark represents the same interval, so keep adding consistently.

Q: Why can't I just estimate where the red point is?

Number lines require exact values, not estimates! The spacing is mathematically precise, so you need to calculate the pattern rather than guess visually.

Q: How do I know if I'm moving left or right correctly?

Moving right means adding positive intervals, moving left means subtracting. Since we go from -3 to 0 (rightward), we add the interval of 1.5 each time.

Number Line Coordinates with Decimal Intervals

What number appears at the point marked in red?

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Understand the problem

What number appears at the point marked in red?

Step-by-step solution

First we need to consider the numbers on the number line from left to right:

$-3,-1.5,0$

Then, we'll try to find the common denominator.

If we use the add 1.5 each time, it will give us the correct sequence numbers:

$-3+1.5=-1.5$

$-\text{1}.5+1.5=0$

Therefore:

$0+1.5=1.5$

Final Answer

1.5

Key Points to Remember

Essential concepts to master this topic

Pattern Recognition: Find the constant interval between consecutive labeled points
Technique: Add interval repeatedly: -3 + 1.5 = -1.5, then -1.5 + 1.5 = 0
Check: Verify pattern continues: 0 + 1.5 = 1.5 matches red point position ✓

Common Mistakes

Avoid these frequent errors

Not finding the consistent interval pattern
Don't randomly guess numbers or subtract instead of add = wrong coordinate! This ignores the systematic spacing between points. Always find the interval by calculating the difference between consecutive labeled points first.

Practice Quiz

Test your knowledge with interactive questions

All negative numbers appear on the number line to the left of the number 0.

FAQ

Everything you need to know about this question

How do I find the interval between points on a number line?

Look at two consecutive labeled points and subtract the smaller from the larger. For example: $-1.5 - (-3) = -1.5 + 3 = 1.5$

What if the red point is between two unlabeled points?

First establish the pattern using labeled points, then extend it step by step. Each tick mark represents the same interval, so keep adding consistently.

Why can't I just estimate where the red point is?

Number lines require exact values, not estimates! The spacing is mathematically precise, so you need to calculate the pattern rather than guess visually.

How do I know if I'm moving left or right correctly?

Moving right means adding positive intervals, moving left means subtracting. Since we go from -3 to 0 (rightward), we add the interval of 1.5 each time.

What if the interval isn't a nice decimal like 1.5?

The same method works! Calculate the exact difference between labeled points, even if it's a fraction like $\frac{2}{3}$ or decimal like 0.75.

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