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#1 2021-05-01 10:44:09
- mathland
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- Registered: 2021-03-25
- Posts: 444
Find Three Additional Points
Use the slope of the line and the point on the line to find
three additional points through which the line passes.
(There are many correct answers.)
1. m = 0, (3, −2)
2. m is undefined, (2, 14)
I know the point-slope formula is needed here one way or another.
If so, how do I use the point-slope formula to answer both questions?
Thanks
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#2 2021-05-01 11:41:30
Re: Find Three Additional Points
Consider a line with m = 0 (i.e. zero gradient). What does that look like?
Now consider a line with undefined gradient*. What does that look like?
*Note that the term 'undefined gradient' can have a different interpretation but since we know it is a straight line we can get away with it here.
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#3 2021-05-01 20:16:00
- Bob
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- Registered: 2010-06-20
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Re: Find Three Additional Points
If you look at my answer to your 'parallel or at right angles' post you'll see that to calculate a gradient we need up/across.
This works fine for all lines except when the line goes straight up. Then you cannot say what the 'up' amount is and the across is zero.
Some might say the gradient is infinite, but mathematicians are very cautious about treating infinity as a number so a better way to describe such a gradient is to call it undefined. ie. The usual definition of gradient doesn't apply in such a case. So the undefined gradient is a vertical line.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob 
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#4 2021-05-02 06:35:39
- mathland
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- Registered: 2021-03-25
- Posts: 444
Re: Find Three Additional Points
Consider a line with m = 0 (i.e. zero gradient). What does that look like?
Now consider a line with undefined gradient*. What does that look like?
*Note that the term 'undefined gradient' can have a different interpretation but since we know it is a straight line we can get away with it here.
1. A line with m = 0 is a horizontal line.
2. A line with a gradient that is undefined has a vertical line.
Yes?
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#5 2021-05-02 06:38:34
- mathland
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- Registered: 2021-03-25
- Posts: 444
Re: Find Three Additional Points
If you look at my answer to your 'parallel or at right angles' post you'll see that to calculate a gradient we need up/across.
This works fine for all lines except when the line goes straight up. Then you cannot say what the 'up' amount is and the across is zero.
Some might say the gradient is infinite, but mathematicians are very cautious about treating infinity as a number so a better way to describe such a gradient is to call it undefined. ie. The usual definition of gradient doesn't apply in such a case. So the undefined gradient is a vertical line.
Bob
Hi Bob.
1. A line with m = 0 is a horizontal line.
2. A line with a gradient that is undefined has a vertical line.
Yes?
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#7 2021-05-03 09:00:21
- mathland
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- Registered: 2021-03-25
- Posts: 444
Re: Find Three Additional Points
Correct.
So you want a horizontal line which passes through (3, -2) and a vertical line which passes through (2, 14). What other points might lie on these lines? Is there a pattern?
If there is a pattern, it's not clear to me.
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#9 2021-05-03 11:33:20
- mathland
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- Registered: 2021-03-25
- Posts: 444
Re: Find Three Additional Points
Try plotting the point (3, -2) on a graph -- then draw a horizontal line through it. Once you've done this, can you identify some other points on the line?
Now, I get it. There are endless points on the horizontal line that goes through the point (3, -2). By the way, the line is y = -2.
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