Question

A line is passing through the points $(6,4)$ and $(6,0)$. At what point will it intersect the $y-$ axis?

• A. $(0,1)$
• B. Line will meet $y$-axis at $(0,0)$
• C. Line will never meet the $y-$axis
• D. $(1,0)$

Answer 1

The correct option is C Line will never meet the $y-$axis

Concept:
Calculate the slope of the line and compare it with the $y$-axis.

If the slope of line is not defined, then line will never meet the $y-$axis.

Plot the points on the cartesian plane for better understanding.

We know that, slope of the line segment whose end point coordinates are $(x_1,y_1)$ and $(x_2,y_2)$ is given by
$\frac{y_2-y_1}{x_2-x_1}$

Here, $(x_1,y_1)\equiv (6,0)$
$(x_2,y_2)\equiv (6,4)$
$\therefore$ Slope of line segment $AB=\frac{4-0}{6-6}$
$=\frac{4}{0}=\text{undefined}$

Hence, the slope of the line $AB$ is not defined.
So, slope of $y-$ axis is not defined.

Hence, Line AB is parallel to $y-$ axis and will never meet with it.
Option (c) is correct.