Answer:
Example of an equation with an undefined slope: x = 2
Step-by-step explanation:
The standard form of linear equations with an undefined slope is x = a, whose graph represents a vertical line. The value of a in the standard form is the x-intercept, (a, 0).
The slope is the ratio of the vertical change in y-values to the horizontal change in x-values.
[tex]\displaystyle\mathsf{Slope(m) =\:\frac{\triangle y}{\triangle x}\:=\frac{y_2 - y_1}{x_2 - x_1}}[/tex]
The slope of a vertical line is undefined because if we were to solve its slope, the denominator will be zero. As we know, division by zero is an undefined operation.
For example, suppose that we have the following points (2, 5) (2, 10).
Let (x₁, y₁) = (2, 5)
(x₂, y₂) = (2, 10)
Substitute these values into the slope formula:
[tex]\displaystyle\mathsf{Slope(m) =\:\frac{\triangle y}{\triangle x}\:=\frac{y_2 - y_1}{x_2 - x_1}\:=\:\frac{10\:-\:5}{2\:-\:2}\:=\frac{5}{0}}[/tex]
Dividing the numerator, 5, by the denominator, 0, will have an undefined quotient.
Thus, the equation of the vertical line will be: x = 2, where a = 2.
