What is the equation of the straight line passing through (5 , -2) and (-4 , 7) ?

Options

A. 5x - 2y = 4
B. `-4x + 7y = 9`
C. `x + y = 3`
D. `x - y = -1`

Answer

To find the equation of the straight line passing through the points (5, -2) and (-4, 7), we can use the formula for the equation of a line given two points.

### Step-by-Step Solution:

1. **Identify the Points**:
Let point A be (x1, y1) = (5, -2) and point B be (x2, y2) = (-4, 7).

2. **Use the Line Equation Formula**:
The equation of the line passing through two points is given by:
\[ y - y1 = \frac{y2 - y1}{x2 - x1} \cdot (x - x1) \]

3. **Substitute the Values**:
Substitute the values of the points into the formula:
\[ y - (-2) = \frac{7 - (-2)}{-4 - 5} \cdot (x - 5) \]
Simplifying this gives:
\[ y + 2 = \frac{7 + 2}{-4 - 5} \cdot (x - 5) \]
\[ y + 2 = \frac{9}{-9} \cdot (x - 5) \]
\[ y + 2 = -1 \cdot (x - 5) \]

4. **Distribute and Rearrange**:
Distributing the -1:
\[ y + 2 = -x + 5 \]
Now, rearranging gives:
\[ y = -x + 5 - 2 \]
\[ y = -x + 3 \]

5. **Final Equation**:
The equation of the line in slope-intercept form is:
\[ y = -x + 3 \]
This can also be written as:
\[ x + y = 3 \]

### Conclusion:
Thus, the equation of the straight line passing through the points (5, -2) and (-4, 7) is \( x + y = 3 \).

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