Consider the statement p : If slope of a straight line is 1 then it is equally inclined to both the axes.
Then, the contrapositive of the statement p is

Options

A. If a straight line is equally inclined to both the axes then its slope is 1
B. If a straight line is equally inclined to both the axes then its slope is not 1
C. If a straight line is not equally inclined to both the axes then its slope is not 1
D. If a straight line is not equally inclined to both the axes then its slope is 1

Answer

To find the contrapositive of the statement \( p \): "If the slope of a straight line is 1, then it is equally inclined to both the axes," we can follow these steps:

### Step 1: Identify the components of the statement
The statement \( p \) can be broken down into two parts:
- Hypothesis (antecedent): "The slope of a straight line is 1" (let's denote this as \( A \))
- Conclusion (consequent): "It is equally inclined to both the axes" (let's denote this as \( B \))

### Step 2: Write the contrapositive
The contrapositive of a statement of the form "If \( A \), then \( B \)" is "If not \( B \), then not \( A \)".

### Step 3: Negate both parts
- Negation of \( B \): "It is not equally inclined to both the axes" (let's denote this as \( \neg B \))
- Negation of \( A \): "The slope of a straight line is not 1" (let's denote this as \( \neg A \))

### Step 4: Combine the negated parts into the contrapositive statement
Thus, the contrapositive of the statement \( p \) is:
"If a straight line is not equally inclined to both the axes, then its slope is not 1."

### Final Answer
The contrapositive of the statement \( p \) is:
**"If a straight line is not equally inclined to both the axes, then its slope is not 1."**

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