Slope of the line joining the points (2,3) and (k,5) is 2,then k = _______

Options

A. 0
B. 3
C. 6
D. 9

Answer

To find the value of \( k \) such that the slope of the line joining the points \( (2, 3) \) and \( (k, 5) \) is equal to 2, we can follow these steps:

### Step 1: Write down the formula for the slope of a line
The slope \( m \) of a line joining two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

### Step 2: Substitute the given points into the slope formula
Here, we have:
- \( (x_1, y_1) = (2, 3) \)
- \( (x_2, y_2) = (k, 5) \)

Substituting these values into the slope formula:
\[ m = \frac{5 - 3}{k - 2} \]

### Step 3: Set the slope equal to the given value
We know that the slope \( m \) is equal to 2. Therefore, we can set up the equation:
\[ \frac{5 - 3}{k - 2} = 2 \]

### Step 4: Simplify the left side of the equation
Calculating the numerator:
\[ 5 - 3 = 2 \]
So we have:
\[ \frac{2}{k - 2} = 2 \]

### Step 5: Cross-multiply to solve for \( k \)
Cross-multiplying gives:
\[ 2 = 2(k - 2) \]

### Step 6: Distribute and simplify
Distributing the 2 on the right side:
\[ 2 = 2k - 4 \]

### Step 7: Solve for \( k \)
Adding 4 to both sides:
\[ 2 + 4 = 2k \]
\[ 6 = 2k \]
Now, divide both sides by 2:
\[ k = 3 \]

### Final Answer
Thus, the value of \( k \) is:
\[ \boxed{3} \]