Question

How do you find the slope of the line \[x = 2\]?

Answer 1

Hint: We know that, the slope between two points \[({x_1},{y_1})\] and \[({x_2},{y_2})\] is \[\dfrac{{{y_1} - {y_2}}}{{{x_1} - {x_2}}}\].
Substitute the value \[x = 2\] in the given equation we can find the slope of the given straight line.
The given line is a vertical line.
Vertical line is one that goes straight up and down, parallel to the y-axis of the coordinate plane. All points on the line will have the same x-coordinate.

Complete step-by-step solution:
It is given that; the equation of line is \[x = 2\].
We have to find the slope of the equation.
We know that the equation for slope is \[\dfrac{{{y_1} - y}}{{{x_1} - x}}\] .
Since, the equation is \[x = 2\], we can substitute this value into \[\dfrac{{{y_1} - y}}{{{x_1} - x}}\]
Simplifying this equation, we get,
\[\dfrac{{{y_1} - y}}{{2 - 2}}\]
It implies, the denominator is zero. So, the slope is undefined.

Hence, the slope of \[x = 2\] is undefined.
A vertical line has no slope.

Note: In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. Slope is often denoted by the letter \[m\].
The slope of a line in the plane containing the \[x\] and \[y\] axes is generally represented by the letter \[m\], and is defined as the change in the \[y\] coordinate divided by the corresponding change in the \[x\] coordinate, between two distinct points on the line.
The slope between two points \[({x_1},{y_1})\] and \[({x_2},{y_2})\]is \[\dfrac{{{y_1} - {y_2}}}{{{x_1} - {x_2}}}\].
If a line has the equation \[x = k\], where \[k\] is a constant, it is a vertical line. A vertical line has an undefined slope.