Question

How do you find the slope of \[x = 5\]?

Answer 1

Hint: Here, we will compare the given equation of a line with the standard equation of a line to find the type of line. Then by using the slope of a line using two points formula, we will find the slope of the line. The slope is defined as the ratio of change in the \[y\] to the change in the \[x\].

Formula Used:
Slope of the line passing through two points is given by the formula \[m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\] where \[\left( {{x_1},{y_1}} \right)\] and \[\left( {{x_2},{y_2}} \right)\] are the coordinates of the points respectively.

Complete Step by Step Solution:
We are given an equation of a line as \[x = 5\].
We know that the standard equation of a line is \[ax + by = c\].
On comparing the given equation to the standard equation of the line, we can say that the value of \[x\] is always \[5\] because the equation of a line does not have the variable \[y\].
So, the equation of a line is independent of the variable \[y\].
Thus, clearly, the equation of a line is the equation of a vertical line.
Now, by using the slope of a line through two points formula \[m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\], we get
\[m = \dfrac{{{y_2} - {y_1}}}{{5 - 5}} = \dfrac{{{y_2} - {y_1}}}{0}\]
We know that any quantity divided by zero is undefined. So, we have the slope is undefined for the vertical line.

Therefore, the slope is undefined for the equation of line \[x = 5\].

Note:
We know that Slope can be represented in the parametric form and in the point form. A point crossing the x-axis is called an x-intercept and A point crossing the y-axis is called the y-intercept. The slope of a line is used to calculate the steepness of a line. We know that the horizontal line does not run vertically i.e., \[{y_2} - {y_1} = 0\] , so the slope is zero and also the vertical line does not run horizontally i.e., \[{x_2} - {x_1} = 0\], the slope is undefined. These slopes are obtained by using the slope of a line using two points formula.