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.