Question

Consider the equation $y-y_1=m(x-x_1)$. If m and $x_1$ are fixed and different lines are drawn for different values of $y_1$, then

• A. The lines will pass through a fixed point
• B. There will be a set of parallel lines
• C. All the lines intersect the line $x=x_1$
• D. All the lines will be parallel to the line $y=x_1$

Answer 1

Answer: (B), (C)

The correct options are
B There will be a set of parallel lines
C All the lines intersect the line $x=x_1$

$y-y_1=m(x-x_1)$
It passes through $(x_1,y_1)$
As $y_1$ is changing, so there is no fixed point
By changing $y_1$, a set of parallel lines will be obtained

Hence, B, C