Question

The equation of straight line passing through point of intersection of the straight lines \[3x - y + 2 = 0,5x - 2y + 7 = 0\] and having infinite slope is
A. \[x = 2\]
B. \[x + y = 3\]
C. \[x = 3\]
D. \[x = 4\]

Answer 1

Hint: A straight line is an infinite, one-dimensional shape with no breadth. The straight line is made up of an infinite number of points linked on both sides of a point. A straight line has no curves. Straight lines can be horizontal, vertical, or slanted. When two or more straight lines meet in a plane, they are referred to as intersecting lines.

Formula Used: Formula for the equation of line using point slope is,
\[y - {y_1} = m\left( {x - {x_1}} \right)\]

Complete step by step solution: The intersection of the straight lines is at point
\[3x - y + 2 = 0,5x - 2y + 7 = 0\]
We have been given that the slope of the required line is
\[ \Rightarrow \infty \]
The necessary line \[AB\] passes through the point of intersection of \[3x - y + 2 = 0\] and \[5x - 2y + 7 = 0\] consequently, identifying the point of intersection:
On solving the below equation concurrently,
\[15x - 5y + 10 = 0\]
\[15x - 6y + 21 = 0\]
We get,
\[y = 11\& x = 3\]
We know that the equation of the line \[AB\]is,
\[y - {y_1} = m\left( {x - {x_1}} \right)\]
Now, we have to substitute the known values in the above equation, we get
\[ \Rightarrow y - 11 = \dfrac{1}{0}(x - 3)\]
On solving the above, we get
\[ \Rightarrow 0 = x - 3\]
Now on further simplification, we get
\[ \Rightarrow x = 3\]
The equation of straight line passing through point of intersection of the straight lines \[3x - y + 2 = 0,5x - 2y + 7 = 0\] and having infinite slope is \[x = 3\]

Option ‘C’ is correct

Note: Students must use extreme caution while inserting the values of the x and y-intercepts in the equations of the line while simultaneously satisfying the required requirements. Furthermore, when a point is on a line, it satisfies the line's equation.