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)

there will be a set of parallel lines
all the lines intersect the line $x=x_1$

All the lines will have a fixed slope $m$ so all lines will be parallel
All lines will be passing through $(x_1,y_1).$

$x_1$ is fixed.

$\therefore x=x_1$ cuts the above lines at $(x_1,y_1).$