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Alja [10]
2 years ago
8

Write an EQUATION with an undefined slope:

Mathematics
1 answer:
Phantasy [73]2 years ago
3 0

Answer:

Example of an equation with an undefined slope: x = 2

Step-by-step explanation:

<h2>Definitions</h2>

The standard form of linear equations with an <u>undefined slope</u> is <em>x</em> = <em>a</em>, whose graph represents a vertical line. The value of a in the standard form is the x-intercept, (<em>a</em>, 0).  

The slope is the ratio of the vertical change in y-values to the horizontal change in x-values.

\displaystyle\mathsf{Slope(m) =\:\frac{\triangle y}{\triangle x}\:=\frac{y_2 - y_1}{x_2 - x_1}}

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.  

<h2>Example:</h2>

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:

\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}}

Dividing the numerator, 5, by the denominator, 0, will have an undefined quotient.

Thus, the equation of the <u>vertical line</u> will be: x = 2, where <em>a</em> = 2.

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