Question

Consider the equation $y-y_1=m(x-x_1)$. In this equation, 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 single point
• B. there will be one possible line only
• C. there will be a set of parallel lines
• D. None of the above

Answer 1

The correct option is C there will be a set of parallel lines

Given equation $y-y_1=m(x-x_1)$
$x_1,m$ is fixed.
So if we change the value of $y_1$ to $y_2$ the line equation will be
$y-y_2=m(x-x_1)$
$\therefore$ Lines will be parallel and all line will intersect the line $x=x_1$ with same angle.