Question

How do you find the slope of \[x=6\]?

Answer 1

Hint: The standard form of the equation of the straight line is \[ax+by+c=0\]. We can find the slope of the line by using the values of the coefficients of the equation. The slope of the line is \[\dfrac{-a}{b}\]. To find the slope of a straight line we have to convert it to its standard form.

Complete step by step answer:
We are given the equation of the straight line as \[x=6\].
We know that the standard form of the equation of the straight line is \[ax+by+c=0\], To convert a straight-line equation to its standard form, we need to take all its terms to one side of the equation leaving zero to the other side. We can do this for the given equation as follows,
Subtracting 6 from both sides of this equation \[x=6\], we get
\[\begin{align}
  & \Rightarrow x-6=6-6 \\
 & \Rightarrow x-6=0 \\
\end{align}\]
This is the standard form of the straight-line equation. Here, we have \[a=1,b=0\And c=-6\]. We can find the slope of the straight-line using the coefficients of the equation as follows
The slope of the line equals \[\dfrac{-a}{b}\], substitute the values of coefficients, we get
\[\Rightarrow slope=\dfrac{-1}{0}\]
If the denominator of a fraction is zero, then its value is undefined/ \[\infty \]. Hence, the slope of the given line is undefined.
We can also plot the graph of the straight line as follows,

Note: We can save out time by remembering the following results:
If the equation of the line is of the type \[y=a\], then the slope of the line is zero, and it is parallel to the X-axis.
If the equation of the line is of the type \[x=a\], then the slope of the line is undefined, and it is parallel to the Y-axis.