Question

How do you find the slope for $x=8?$

Answer 1

Hint: To find the slope for $x=8$ firstly calculate slope by dividing the change in the $y$-value between two points over the change in the $x$-value

Complete step-by-step answer:
Given in the problem that find the slope for $x=8$
Here, $x=8$ is the equation of the vertical line.
Slope is defined as change in $y$ to the corresponding change in $x.$
$slope=\dfrac{\text{change in }y}{\text{corresponding change in }x}$
Here, from equation $x=8$. We conclude that the value of $x$ does not change. This means the change in $x$ value is always $'0'$
Also we know that the slope of the vertical line is undefined. Therefore the slope of line of equation $x=8$ is undefined.
Let us draw a graph for $x=8$

From the graph it can be conclude that,
$slope=\dfrac{Rise}{Run}=\dfrac{\infty }{0}$

Therefore, from the graph also it is seen that the slope for $x=8$is undefined. Since it is a vertical line.

Additional Information:
One of the most important things to understand about lines is the definition of slope. Slope is the ‘steepness’ of the line. It is also called a gradient. It can be calculated by dividing the change in the $y$value between two points over the change in the $x$-value. It is also commonly called rise over run.
Formula of slope $(m)$ can be written as.
$m=\dfrac{rise}{run}=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}=\dfrac{\Delta y}{\Delta x}$
Where, $m=$ slope
$\left( {{x}_{1}},{{y}_{1}} \right)=$ coordinates of first point in the line.
$\left( {{x}_{2}},{{y}_{2}} \right)=$ Coordinates of second point in the line.
Slope can also be directly calculated from the graph.

Note:
The slope of any vertical line having any $x$ value is undefined. It is not similar for horizontal lines. Since, the slope of the horizontal line is zero which is not undefined.