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The problem is asking you to fill in the values for the table and plot the graph of the linear equation \( y = 2x + 5 \).

Let's calculate the values of \( y \) for each value of \( x \) given in the table:

1. **When \( x = -2 \):**
   \[
   y = 2(-2) + 5 = -4 + 5 = 1
   \]

2. **When \( x = -1 \):**
   \[
   y = 2(-1) + 5 = -2 + 5 = 3
   \]

3. **When \( x = 0 \):**
   \[
   y = 2(0) + 5 = 0 + 5 = 5
   \]

4. **When \( x = 1 \):**
   \[
   y = 2(1) + 5 = 2 + 5 = 7
   \]

5. **When \( x = 2 \):**
   \[
   y = 2(2) + 5 = 4 + 5 = 9
   \]

Now, let's fill in the table with these values:

\[
\begin{array}{c|c|c|c|c|c}
x & -2 & -1 & 0 & 1 & 2 \\
\hline
y & 1 & 3 & 5 & 7 & 9 \\
\end{array}
\]

To draw the graph, plot these points on the coordinate grid: 
- \((-2, 1)\)
- \((-1, 3)\)
- \((0, 5)\)
- \((1, 7)\)
- \((2, 9)\)

These points will form a straight line since the equation \( y = 2x + 5 \) represents a linear function.

Would you like any further details or have any questions? Here are some related questions:

1. How do you determine the slope of a line from its equation?
2. What is the y-intercept of the equation \( y = 2x + 5 \)?
3. How would you plot a graph for a quadratic function?
4. How does the value of the coefficient \(2\) affect the graph's steepness?
5. What are some other methods to graph a linear equation?

**Tip:** Remember, the coefficient of \(x\) in a linear equation \(y = mx + b\) is the slope, and it shows how steep the line is.

Learn how to graph the linear equation y = 2x + 5 by filling in a table of values and plotting the points on a coordinate grid. This problem helps students understand algebraic concepts, graphing linear equations, and interpreting slope and intercepts. Suitable for students in Grades 7-9.

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