Consider the equation `y-y_1=m(x-x_1)` . If `ma n dx_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`

Options

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 these

Answer

C

Explanation

We have , `y-y_(1)=m(x-x_(1))` , where m and `x_(1)` are fixed . Therefore, the system represents a set of parallel lines of slope m.