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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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Answer:

"f(x) = 4(1.02)7x; spreads at a rate of approximately 2% daily"

Step-by-step explanation:

<u>Complete Question:</u>

A virus that initially infected four people is spreading at a rate of 15% each week. The following function represents the weekly spread of the virus: f(x) = 4(1.15)x. Rewrite the function to show how quickly the virus spreads each day and calculate this rate as a percentage.

f(x) = 4(1.15)7x; spreads at a rate of approximately 1.5% daily

f(x) = 4(1.02)7x; spreads at a rate of approximately 2% daily

f(x) = 4(1.157)x; spreads at a rate of approximately 2.66% daily

f(x) = 4(1.02)x; spreads at a rate of approximately 0.2% daily

<u>Solution:</u>

The weekly number of people infected would be:

f(x)=4(1.15)^x

7 days in a week, so daily number of people infected would be:

f(x)=4(1+r)^{7x}

To find daily rate, we set these 2 equations equal and solve for r:

4(1.15)^x=4(1+r)^{7x}\\1.15^x=(1+r)^{7x}\\1.15^x=((1+r)^7)^x\\1+r=1.02\\r=1-1.02=0.02

That is 0.02*100 = 2% daily

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