https://file.aiquickdraw.com/mathbot/file/1729002354677fhn7tcjs.jpg

To solve this, we need to determine which graph corresponds to the equation:

\[
5x + 2y = 10
\]

### Step 1: Solve for \( y \)
To put this equation in slope-intercept form \( y = mx + b \) (where \( m \) is the slope and \( b \) is the y-intercept), we isolate \( y \).

\[
5x + 2y = 10
\]
\[
2y = -5x + 10
\]
\[
y = -\frac{5}{2}x + 5
\]

Now we have the equation \( y = -\frac{5}{2}x + 5 \).

### Step 2: Identify key features
- **Slope**: The slope \( m = -\frac{5}{2} \). This means the line goes down by 5 units for every 2 units it moves to the right.
- **Y-intercept**: The y-intercept is \( 5 \), so the line crosses the y-axis at \( (0, 5) \).

### Step 3: Compare with the graphs
We are looking for:
- A graph with a negative slope (sloping downward from left to right).
- A line that crosses the y-axis at \( 5 \).

From the images, the correct graph is the **bottom-right graph**, which shows a line with a negative slope and a y-intercept at \( (0, 5) \).

Would you like more details, or do you have any questions?

---

Here are 5 related questions for practice:
1. How would the graph change if the slope was \( -\frac{3}{2} \) instead of \( -\frac{5}{2} \)?
2. What would happen to the graph if the y-intercept changed from 5 to 3?
3. How can you check if a point lies on the line \( 5x + 2y = 10 \)?
4. What is the x-intercept of the equation \( 5x + 2y = 10 \)?
5. How would the graph look if the equation were \( 5x + 2y = 0 \)?

### Tip:
Always convert the equation to slope-intercept form when graphing, as it makes it easier to understand the line's slope and intercepts.

Which graph shows the equation 5x + 2y = 10?

Identify the graph of the linear equation 5x + 2y = 10 by transforming it into slope-intercept form. Understand the slope and y-intercept to match the correct graph. Suitable for students in Grades 8-10.

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