Math Is Fun Forum

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Slope and inclination

Find slope and inclination  of points (3,-2)  (2,7)

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Malik

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Slope and inclination

Make a coordinate diagram like the one I have just made for the Pythagoras question.

I'll use the same letters as in that diagram.

Calculate CA and BC.

The slope is given by

This will also be the tangent of the angle of inclination, so use

where ATAN means the inverse tangent

Bob

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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

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Slope and inclination

,slope = -9 and aphha =tann inverse -9

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Malik

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Slope and inclination

Uff how to remember these formulas ex slope intersept normal slope point slope eq of straight line and alll slopes formulas slope of straight line etc

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Malik

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Slope and inclination

-9 is correct.

Slope is always up/across.

intercept means where a line crosses.

These pages are good, and they have interactive graphs to experiment with.

http://www.mathsisfun.com/equation_of_line.html

http://www.mathsisfun.com/data/straight_line_graph.html

Bob

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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

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Slope and inclination

And alpha is -83.68 degree why we add 180 in this ans what reason

Why slope is change in y divide by change in x

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Malik

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Slope and inclination

Here is a diagram showing the line, slope and angle:

Your calculated angle is correct.  But, unless you are told otherwise, it is normal to measure angles on graphs, clockwise from the positive x axis.  If you do +180 - 83.68 you will get the required obtuse angle.

Why slope is change in y divide by change in x

I suppose you could have a new word, let's say epols, which is calculated by change in x divided by change in y.  It is just a matter of definition.  But calculating the slope by dy/dx means that the value will go up as the line gets steeper.  So it makes sense to define slope this way.  And it is similar* to the way geographers work out the steepness of a hillside, and road signs show that the roadway is sloping ahead.

In maths, some things are just defined a certain way and we agree to stick to that.  eg.  why is x across and y up?  why are vectors written like this

and not like this

Bob

* Ok it's not exactly the same in geography, but let's not complicate things any more than necessary

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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

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Slope and inclination

Where is -83 degree in degree measure tool

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Malik

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Slope and inclination

Do you mean in Geogebra?  You need to display the tools and customise to include the angle tool.  (I think???) I use Geometer's Sketchpad.

bobbym will know for sure.

Bob

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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

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Slope and inclination

why is x across and y up?  why are vectors written like this
Submit
and not like this
Submit

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Malik

Zeeshan 01

Member

Registered: 2016-07-22

Posts: 746

Re: Slope and inclination

[2 by 1 ]and not[ 2 1]

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Malik

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Slope and inclination

What I am trying to say is "It could be either".  Someone had to decide and that's what they chose.  Descartes https://en.wikipedia.org/wiki/Ren%C3%A9 … cal_legacy invented the x-y coordinate system and everyone has kept to his definition.

Bob

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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