Question

Which of the following equations of line have undefined slope?

• A. $y=4$
• B. $x=3$
• C. $2x+3y-1=0$
• D. $x=3y$

Answer 1

The correct option is B $x=3$

Concept: If a line is parallel to $y$-axis, then the slope of the line is undefined.

Option(a): $y=4$
This line is parallel to $x-$ axis. Hence the slope of line is equal to slope of $x$-axis which is $0$.

Option(b): $x=3$
This line is parallel to $y-$ axis. Hence the slope of line is equal to slope of $y$-axis which is undefined.

Option (c): $2x+3y-1=0$
Convert this to the slope intercept form of a line which is $y=mx+b$ where 'm' is the slope and 'b' is the intercept of the line.

Simplify the equation $2x+3y-1=0$
$3y=-2x+1$
$y=\frac{-2x}{3}+\frac{1}{3}$
On comparing the above equation with $y=mx+b$, we get,
$\text{slope},m=\frac{-2}{3}$.

Option (d): $x=3y$
Convert this to the slope intercept form of a line which is $y=mx+b$ where 'm' is the slope and 'b' is the intercept of the line.

Simplify the equation $x=3y$
$y=\frac{x}{3}$
On comparing the above equation with $y=mx+b$, we get,
$\text{slope},m=\frac{1}{3}$.

Hence, Option (b) is correct.