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# GEOMETRY

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Write an equation of a line with undefined slope that passes through the point(3,-2)

BOSEOK  Sep 17, 2017
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y=-2.

Because the line is horizontal, the slope is undefined.

Gh0sty15  Sep 17, 2017
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How can I know that line is horizontal?

BOSEOK  Sep 17, 2017
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The slope of a horizontal line is well defined- it is zero.

I think what is wanted is as follows:

General equation of a straight line is y =mx + c

Here we know that this line goes through point (3, -2) so we can say

-2 = m*3 + c

This means c = -2 - 3m.  Put this in the equation for the line:

y = mx - 2 - 3m

or

y = m(x - 3) - 2

The slope m is undefined.

Alan  Sep 17, 2017
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BOSEOK  Sep 17, 2017
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Ok. x = 3 is a vertical line.  This has infinite slope, so is basically undefined.

(I repeat: a horizontal line has zero slope).

Alan  Sep 17, 2017
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To put it simply, in linear equations, if an equation is y= (any real number), then it is horizontal. For example, y=2 is horizontal, and it has an undefined slope. x=3 is actually a vertical line. Its slope is 0.

Correct me if I'm wrong.

Gh0sty15  Sep 17, 2017
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BOSEOK is correct; the equation is x=3.

Contrary to what Gh0sty stated, the slope is defined when a linear function happens to be horizontal. Let's figure out the slope of the graph provided by Gh0sty. I will use the points $$(3,-2)$$ and $$(0,-2)$$. Let's find the slope.

Of course, the formula for slope is the following:

$$m=\frac{y_2-y_1}{x_2-x_1}$$

 $$m=\frac{-2-(-2)}{0-3}$$ Continue to simplify the fraction. $$m=\frac{0}{-3}=0$$

The slope is 0. 0 is a valid number for the slope. If you type into Demos y=0x-2, the line will appear exactly as the picture above.

Let's try calculating the slope of the line x=-3. Two arbitrary points on the line are $$(-3,2)$$ and $$(-3,0)$$

What is the slope of this? Let's try using the formula again. Let's see what happens.

 $$\frac{0-2}{-3-(-3)}$$ Simplify both the numerator and the denominator. $$\frac{-2}{0}$$

Of course, any number divided by 0 is undefined and therefore it has an undefined slope.

Therefore, BOSEOK's answer is correct because it meets both criteria of

1) A line with an undefined slope

2) A line that passes through the point $$(3,-2)$$

And therefore, $$x=3$$ is correct.

TheXSquaredFactor  Sep 17, 2017
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Hey...I was wrong. (Again.)

Sorry Boseok.

Gh0sty15  Sep 17, 2017
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Sorry Alan.

Gh0sty15  Sep 17, 2017
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No problem! Don't worry about it.

Alan  Sep 17, 2017

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