The equation of straight line passing through the point of intersection of the straight line `3x – y +2=0` and `5x - 2y +7=0` and having infinite slope is

Options

A. `x=2`
B. `x=3`
C. `x=4`
D. `x+y=3`

Answer

To solve the problem, we need to find the equation of the straight line that passes through the point of intersection of the two given lines and has an infinite slope. An infinite slope indicates that the line is vertical.

### Step-by-Step Solution:

1. **Identify the Given Lines**:
The equations of the lines are:
\[ 3x - y + 2 = 0 \quad \text{(Equation 1)} \]
\[ 5x - 2y + 7 = 0 \quad \text{(Equation 2)} \]

2. **Find the Point of Intersection**:
We will use the elimination method to find the intersection point of the two lines. First, we can manipulate the equations to eliminate one variable. We can multiply Equation 1 by 2 to align the coefficients of \(y\):
\[ 2(3x - y + 2) = 0 \implies 6x - 2y + 4 = 0 \quad \text{(Modified Equation 1)} \]

3. **Subtract the Modified Equation from Equation 2**:
Now we subtract Equation 2 from the Modified Equation 1:
\[ (6x - 2y + 4) - (5x - 2y + 7) = 0 \]
Simplifying this gives:
\[ 6x - 5x - 2y + 2y + 4 - 7 = 0 \implies x - 3 = 0 \]
Thus, we find:
\[ x = 3 \]

4. **Substitute \(x\) back to find \(y\)**:
Now we substitute \(x = 3\) back into either of the original equations to find \(y\). Let's use Equation 1:
\[ 3(3) - y + 2 = 0 \implies 9 - y + 2 = 0 \implies 11 - y = 0 \implies y = 11 \]
Therefore, the point of intersection is:
\[ (3, 11) \]

5. **Write the Equation of the Line with Infinite Slope**:
A line with an infinite slope is a vertical line. The equation of a vertical line passing through the point \((3, 11)\) is:
\[ x = 3 \]

### Final Answer:
The equation of the straight line passing through the point of intersection of the given lines and having an infinite slope is:
\[ \boxed{x = 3} \]