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The question asks to **draw the graph of the equation** \(5x + 2y = 10\) for values of \(x\) from \(-2\) to \(4\). Let’s break it down step by step:

### 1. Rearrange the Equation:
We need to solve for \(y\) in terms of \(x\):
\[
5x + 2y = 10
\]
Subtract \(5x\) from both sides:
\[
2y = 10 - 5x
\]
Now, divide by 2:
\[
y = \frac{10 - 5x}{2}
\]
\[
y = 5 - \frac{5x}{2}
\]

### 2. Generate Coordinates:
Now, let's plug in the values of \(x\) from \(-2\) to \(4\) and calculate the corresponding \(y\)-values.

- For \(x = -2\):
  \[
  y = 5 - \frac{5(-2)}{2} = 5 + 5 = 10
  \]
  So, \((-2, 10)\).

- For \(x = -1\):
  \[
  y = 5 - \frac{5(-1)}{2} = 5 + \frac{5}{2} = 5 + 2.5 = 7.5
  \]
  So, \((-1, 7.5)\).

- For \(x = 0\):
  \[
  y = 5 - \frac{5(0)}{2} = 5
  \]
  So, \((0, 5)\).

- For \(x = 1\):
  \[
  y = 5 - \frac{5(1)}{2} = 5 - 2.5 = 2.5
  \]
  So, \((1, 2.5)\).

- For \(x = 2\):
  \[
  y = 5 - \frac{5(2)}{2} = 5 - 5 = 0
  \]
  So, \((2, 0)\).

- For \(x = 3\):
  \[
  y = 5 - \frac{5(3)}{2} = 5 - 7.5 = -2.5
  \]
  So, \((3, -2.5)\).

- For \(x = 4\):
  \[
  y = 5 - \frac{5(4)}{2} = 5 - 10 = -5
  \]
  So, \((4, -5)\).

### 3. Plot the Points:
You will plot the points \((-2, 10)\), \((-1, 7.5)\), \((0, 5)\), \((1, 2.5)\), \((2, 0)\), \((3, -2.5)\), and \((4, -5)\) on the grid provided in the question. Then, draw a straight line through these points to represent the equation \(5x + 2y = 10\).

### Does that help? Do you want me to explain how to plot these points or any other detail?

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Here are some related questions to explore further:

1. How would you find the intercepts of the equation \(5x + 2y = 10\)?
2. What happens to the graph if you change the equation to \(5x + 2y = 15\)?
3. How do you calculate the slope of the line given by \(5x + 2y = 10\)?
4. How can you confirm if a specific point lies on the line?
5. How do parallel lines compare in terms of their slopes?

**Tip**: When rearranging an equation into slope-intercept form (\(y = mx + b\)), \(m\) represents the slope of the line and \(b\) is the y-intercept.

On the grid, draw the graph of 5x + 2y = 10 for values of x from -2 to 4.

Learn how to graph the linear equation 5x + 2y = 10 with step-by-step instructions. This problem covers the rearrangement of the equation into slope-intercept form and plotting points for values of x from -2 to 4. Suitable for students in Grades 9-11.

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