Question

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

Answer 1

Hint: 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.