`{:("Quantity A","Quantity B"),("The slope of the line","The slope of the line"),(2x+5y=10,5x+2y=10):}`

Answer

To solve the problem, we need to find the slopes of the two given lines and compare them. Let's go through the steps one by one.

### Step 1: Identify the equations
We have two equations:
1. Quantity A: \( 2x + 5y = 10 \)
2. Quantity B: \( 5x + 2y = 10 \)

### Step 2: Convert Quantity A into slope-intercept form
We need to convert the first equation into the form \( y = mx + c \), where \( m \) is the slope.

Starting with:
\[ 2x + 5y = 10 \]

Subtract \( 2x \) from both sides:
\[ 5y = -2x + 10 \]

Now, divide every term by \( 5 \):
\[ y = -\frac{2}{5}x + 2 \]

From this, we can see that the slope \( m_A \) of Quantity A is:
\[ m_A = -\frac{2}{5} \]

### Step 3: Convert Quantity B into slope-intercept form
Now, let's convert the second equation into slope-intercept form.

Starting with:
\[ 5x + 2y = 10 \]

Subtract \( 5x \) from both sides:
\[ 2y = -5x + 10 \]

Now, divide every term by \( 2 \):
\[ y = -\frac{5}{2}x + 5 \]

From this, we can see that the slope \( m_B \) of Quantity B is:
\[ m_B = -\frac{5}{2} \]

### Step 4: Compare the slopes
Now we have:
- Slope of Quantity A: \( m_A = -\frac{2}{5} \) (which is approximately -0.4)
- Slope of Quantity B: \( m_B = -\frac{5}{2} \) (which is -2.5)

To compare:
- Since \( -0.4 > -2.5 \), we conclude that:
\[ m_A > m_B \]

### Conclusion
Thus, Quantity A (the slope of the line \( 2x + 5y = 10 \)) is greater than Quantity B (the slope of the line \( 5x + 2y = 10 \)).

### Final Answer
**Quantity A is greater than Quantity B.**

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