https://file.aiquickdraw.com/mathbot/file/17285157614600br9nesa.jpg

The image you provided shows a proportionality exercise where you are required to fill in the table and the graph based on the given information:

### Given:
- Constant of Proportionality: \( k = 2 \)
- Equation: \( Y = 2x \)
- Table: The \( x \) values are given as 0, 1, 2, 3, and corresponding \( y \) values are missing.
- The graph is missing.

### Step 1: Filling in the Table
Since the equation is \( Y = 2x \), you can calculate the \( y \)-values by multiplying each \( x \)-value by 2:
- \( x = 0 \), \( y = 2 \times 0 = 0 \)
- \( x = 1 \), \( y = 2 \times 1 = 2 \)
- \( x = 2 \), \( y = 2 \times 2 = 4 \)
- \( x = 3 \), \( y = 2 \times 3 = 6 \)

So the completed table looks like this:
\[
\begin{array}{c|c}
x & y \\
\hline
0 & 0 \\
1 & 2 \\
2 & 4 \\
3 & 6 \\
\end{array}
\]

### Step 2: Plotting the Graph
You will plot the points \((0,0)\), \((1,2)\), \((2,4)\), and \((3,6)\) on the graph. Since the relationship is proportional and the constant of proportionality is 2, the points will lie on a straight line with a slope of 2.

- The line will pass through the origin \((0,0)\) and have a slope that rises by 2 units on the \(y\)-axis for every 1 unit on the \(x\)-axis.

If you'd like, I can create a graph or explain more in detail how the graph will look like.

Let me know if you would like any clarification or further details!

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Here are 5 related questions you can consider:
1. What does the constant of proportionality \(k = 2\) represent in this context?
2. How would the equation change if the constant of proportionality were 3 instead of 2?
3. Can you explain how the slope of the line in the graph relates to the equation \(Y = 2x\)?
4. How would the graph differ if \(x\) had negative values?
5. How can you identify a proportional relationship from a table or graph?

### Tip:
When plotting a proportional relationship, always check if the graph passes through the origin \((0,0)\) and forms a straight line, as this confirms proportionality.

Fill in the missing pieces below based on the constant of proportionality, table, and graph.

Solve and graph the linear equation Y = 2x with constant proportionality k = 2. Learn to complete the table of values and accurately graph the proportional relationship. This activity covers key concepts in proportionality and linear graphing. Suitable for students in Grades 6-8.

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