The equation of the line passing through the points (5, 3) and (3, 5) is

Options

A. X - Y + 8 = 0
B. X + Y + 8 = 0
C. X - Y - 8 = 0
D. X + Y - 8 = 0

Answer

To find the equation of the line passing through the points (5, 3) and (3, 5), we can use the two-point form of the equation of a line. Let's go through the steps:

### Step 1: Identify the points
We have two points:
- Point A (x1, y1) = (5, 3)
- Point B (x2, y2) = (3, 5)

### Step 2: Use the two-point formula
The two-point formula for the equation of a line is given by:
\[ y - y_1 = \frac{y_2 - y_1}{x_2 - x_1} (x - x_1) \]

### Step 3: Substitute the values
Substituting the values of the points into the formula:
\[ y - 3 = \frac{5 - 3}{3 - 5} (x - 5) \]

### Step 4: Simplify the right side
Calculating the slope:
\[ y - 3 = \frac{2}{-2} (x - 5) \]
\[ y - 3 = -1 (x - 5) \]

### Step 5: Distribute the slope
Distributing -1:
\[ y - 3 = -x + 5 \]

### Step 6: Rearrange the equation
Now, we will rearrange the equation to standard form:
\[ y + x - 5 + 3 = 0 \]
\[ x + y - 8 = 0 \]

### Final Equation
Thus, the equation of the line passing through the points (5, 3) and (3, 5) is:
\[ x + y - 8 = 0 \]

### Conclusion
The correct option is D: \( x + y - 8 = 0 \).

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