If the line passing through `(4,3)a n d(2,k)` is parallel to the line `y=2x+3,` then find the value of `kdot`

Explanation

To solve the problem, we need to find the value of \( k \) such that the line passing through the points \( (4, 3) \) and \( (2, k) \) is parallel to the line given by the equation \( y = 2x + 3 \).

### Step-by-Step Solution:

1. **Identify the slope of the given line**:
The equation of the line is \( y = 2x + 3 \). From this equation, we can see that the slope \( m \) is \( 2 \).

**Hint**: The slope of a line in the form \( y = mx + c \) is simply the coefficient of \( x \).

2. **Calculate the slope of the line through points \( (4, 3) \) and \( (2, k) \)**:
The formula for the slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, we have \( (x_1, y_1) = (4, 3) \) and \( (x_2, y_2) = (2, k) \). Thus, the slope is:
\[ m = \frac{k - 3}{2 - 4} = \frac{k - 3}{-2} = -\frac{k - 3}{2} \]

**Hint**: Remember to substitute the coordinates correctly into the slope formula.

3. **Set the slopes equal**:
Since the two lines are parallel, their slopes must be equal. Therefore, we set the slope of the line through the points equal to the slope of the line \( y = 2x + 3 \):
\[ -\frac{k - 3}{2} = 2 \]

**Hint**: When two lines are parallel, their slopes are equal.

4. **Solve for \( k \)**:
To eliminate the fraction, we can multiply both sides of the equation by \( -2 \):
\[ k - 3 = -4 \]
Now, add \( 3 \) to both sides:
\[ k = -4 + 3 \]
Therefore:
\[ k = -1 \]

**Hint**: Isolate \( k \) by performing inverse operations carefully.

### Final Answer:
The value of \( k \) is \( -1 \).