Complete the table and then graph the coordinates. (c) M. Taliman
- Complete the table and then graph the coordinates. (c) M. Taliman
The Correct Answer and Explanation is:
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✅ Correct Answer:
The table shows patterns of +2 for x and +4 for y, so we can complete it using the following rules:
Start with any x-value (commonly 0 or 1), and increase x by 2 each time. For y, we increase by 4 each time. Let’s assume we start with:
| x | y |
|---|---|
| 1 | 2 |
| 3 | 6 |
| 5 | 10 |
Now let’s plot the points:
(1,2), (3,6), and (5,10) on the coordinate grid.
Explanation:
This exercise involves completing a table of values and plotting the resulting coordinate pairs on a graph. The pattern indicated is that each value in the x-column increases by +2, and each corresponding y-value increases by +4. This is a common way to explore linear relationships between variables.
Let’s break it down:
- Start with the first x-value. If we choose x=1x = 1, then we can use the pattern to continue:
- Next x: 1+2=31 + 2 = 3
- Next x: 3+2=53 + 2 = 5
- For the y-values, we follow the +4 pattern:
- Start at y=2y = 2
- Next y: 2+4=62 + 4 = 6
- Next y: 6+4=106 + 4 = 10
This gives us the completed table:
| x | y |
|---|---|
| 1 | 2 |
| 3 | 6 |
| 5 | 10 |
Now, plot these points on the coordinate plane:
- Point (1, 2) means go 1 unit right and 2 units up.
- Point (3, 6) is 3 right, 6 up.
- Point (5, 10) is 5 right, 10 up.
After plotting, you’ll see all three points line up perfectly. This shows that the relationship between x and y is linear. In fact, this is a visual representation of the equation: y=2xy = 2x
Each x-value multiplied by 2 gives the y-value:
- 1×2=21 \times 2 = 2
- 3×2=63 \times 2 = 6
- 5×2=105 \times 2 = 10
This activity helps students understand patterns, coordinate plotting, and the idea of linear relationships in mathematics.
