Question

How do you graph the line given $\left( {2,4} \right)$, undefined slope?

Answer 1

Here, we will use the definition of an undefined slope to draw a vertical line parallel to the$y$ axis using the equation of the line. Then we will plot the given point on that line to get the required answer. The slope of a line is defined as the value which measures the steepness of the line or the inclination of the line with the $x$ axis.

Complete step by step solution:
As we know, an undefined slope is also known as an infinitely large slope and it is the slope of a vertical line that is parallel to the ordinate or the $y$ axis. Since this line is parallel to the $y$ axis, hence, the $x$ coordinate is fixed and it never changes whereas, the $y$ coordinate can take infinitely possible values on that particular vertical slope.
Now, since we are required to graph an undefined slope consisting of the point $\left( {2,4} \right)$
Hence, we should know that the equation of this slope is $x = c$, where $c$ is the value of the $x$ coordinate which is a constant.
Since, the given point is having $x$ coordinate as $x = 2$
Therefore, the equation of the undefined slope will be $x = 2$
Hence, we will construct the graph as follows:

Note:
A coordinate plane is a two-dimensional number line where the vertical line is called the $y$-axis and the horizontal is called the $x$-axis. These lines are perpendicular and intersect at their zero points. Their intersection point is called the origin and usually denoted as $O$.
A slope of any line can either be a positive number, negative number, zero, or undefined. As we have discussed, the slope of a vertical line that is parallel to the $y$ axis is undefined. Similarly, the slope of a horizontal line that is parallel to the $x$ axis is zero.