The graph shows a linear relation between variable y and x. Consider two quantities p and q defined by the equations.
`p=y/x`
`q=(y-b)/x`
As x changes from zero to a, which of the following statements are correct according to the graph?

A. Quantity p increases and q decrease.
B. Quantity p decrease and q increases
C. Quantity p decreases and q remain constant
D. Quantity p increases and q remain constant.

Options

A. Quantity p increases and q decrease.
B. Quantity p decrease and q increases
C. Quantity p decreases and q remain constant
D. Quantity p increases and q remain constant.

Explanation

To solve the problem, we need to analyze the given quantities \( p \) and \( q \) based on the linear relationship between \( y \) and \( x \) as described.

### Step 1: Understanding the Linear Relationship
The relationship between \( y \) and \( x \) is linear, which can be expressed in the form:
\[ y = mx + b \]
where \( m \) is the slope of the line and \( b \) is the y-intercept.

### Step 2: Analyzing Quantity \( p \)
The quantity \( p \) is defined as:
\[ p = \frac{y}{x} \]
Substituting the expression for \( y \):
\[ p = \frac{mx + b}{x} = m + \frac{b}{x} \]
As \( x \) increases from 0 to \( a \), the term \( \frac{b}{x} \) decreases (since \( b \) is a constant and \( x \) is increasing). Thus, \( p \) decreases as \( x \) increases.

### Step 3: Analyzing Quantity \( q \)
The quantity \( q \) is defined as:
\[ q = \frac{y - b}{x} \]
Substituting the expression for \( y \):
\[ q = \frac{mx + b - b}{x} = \frac{mx}{x} = m \]
Here, \( q \) simplifies to \( m \), which is the slope of the line. Since \( m \) is a constant, \( q \) remains constant as \( x \) changes.

### Step 4: Conclusion
From our analysis:
- \( p \) decreases as \( x \) increases.
- \( q \) remains constant as \( x \) increases.

Thus, the correct statement is:
**C. Quantity \( p \) decreases and \( q \) remains constant.**