Question

Which of the following linear equations has an undefined slope when plotted?
A. $x = 3$
B. $y = 0$
C. $x = - y$
D. $x - y = 0$

Answer 1

Here, we have to find which of the given linear equations has an undefined slope. Slope or gradient of a line can be defined as which specifies both the direction and steepness of a line and is determined by finding the ratio of vertical change to the horizontal change and the statement can be written as $m = \dfrac{{\Delta y}}{{\Delta x}}$ where $m$ is the slope of the line.

Complete step by step answer:
In the question we have to find which of the given linear equations has an undefined slope.Linear equations can be defined as the algebraic equations which have the order equal to unity or one.Slope or gradient of a line can be defined as which specifies both the direction and steepness of a line and is determined by finding the ratio of vertical change to the horizontal change and is represented by the symbol $m$.

The steepness of a line is measured by the absolute value of the shape so the slope with a greater absolute value represents a steeper line. The direction of the line either falls, rises, horizontal or vertical.The slope equation of the line is given by the formula,
$m = \tan \theta \\\ \Rightarrow m = \dfrac{{\Delta y}}{{\Delta x}}$

The slope of the line is undefined if the line is vertical as the vertical line has zero rise and any amount of run.Therefore, the line $x = 3$ has an undefined slope as it is perpendicular to the x-axis.The line $y = 0$ has zero slope.

Hence, option (A) is the correct answer.

Note: A line which extends from left to right has a positive run and positive rise, and also yields a positive slope and a line which declines from left to right has a negative run and negative fall and also gives a negative slope. The horizontal line has a zero positive slope as it has zero rise and positive run.