Question

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

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

Answer 1

The correct option is C

$x=3$

Determine the equation of the line :

Given that: Slope of the required line is $=\infty$

The required line $AB$ passes through the point of intersection of $3x-y+2=0$ and $5x-2y+7=0$

therefore, finding the point of intersection:

Solving the equations simultaneously we get:

$$\begin{gathered} 15x-5y+10=0\&15x-6y+21=0 \\ \therefore y=11\&x=3 \end{gathered}$$

The equation of the line $AB$ is:

$$\begin{gathered} y-y_1=m(x-x_1) \\ \Rightarrow y-11=\frac{1}{0}(x-3) \\ \Rightarrow 0=x-3 \\ \Rightarrow x=3 \end{gathered}$$

Therefore, the correct answer is Option (C).