Find the equation of a straight line passing through (4,5) having slope 1

Explanation

To find the equation of a straight line passing through the point (4, 5) with a slope of 1, we can use the point-slope form of the equation of a line. The point-slope form is given by:

\[ y - y_1 = m(x - x_1) \]

where:
- \( m \) is the slope of the line,
- \( (x_1, y_1) \) is a point on the line.

### Step-by-Step Solution:

1. **Identify the given values**:
- The slope \( m = 1 \).
- The point \( (x_1, y_1) = (4, 5) \).

2. **Substitute the values into the point-slope formula**:
\[ y - 5 = 1(x - 4) \]

3. **Simplify the equation**:
- Distributing the slope on the right side:
\[ y - 5 = x - 4 \]

4. **Rearranging the equation**:
- Add 5 to both sides:
\[ y = x - 4 + 5 \]
- Simplifying further:
\[ y = x + 1 \]

5. **Rearranging into standard form**:
- To write the equation in the standard form \( Ax + By + C = 0 \):
\[ x - y + 1 = 0 \]

### Final Answer:
The equation of the straight line is:
\[ x - y + 1 = 0 \]