Question

Tutorial: Slope

Answer 1

\(\huge\bf Types~of~Slope:\)

\(\bf\small Positive~Slope:\)

Positive slope rises from LEFT to RIGHT.

\(\bf\small Negative~Slope:\)

Negative slope declines from LEFT to RIGHT.

Examples of Positive and Negative Slopes:

http://www.shmoop.com/images/prealgebra/unit6/pa.6.195.png

\(\bf\small No~ Slope:\)

Lines with no slope are horizontal, and parallel to the x-axis.

Example:

http://dj1hlxw0wr920.cloudfront.net/userfiles/wyzfiles/fef7b984-29f7-468a-b78a-2cb5a2124bf9.gif

\(\bf\small Undefined~Slope:\)

Lines with undefined slope are vertical, and parallel to the y-axis.

Example:

http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut27ex5c.gif

\(\huge\bf Finding~Slope:\)

There are 3 different ways to find slope.

\(\bf Equations:\)

Some equations just give you the slope, for example:

\(\bf\small Slope-intercept~form:\)

\(y = \color{lime}mx + \color{blue}b\)

Where \(\color{lime}m\) = slope, and \(\color{blue}b\) = y-intercept.

So if we have:

\(y = \color{lime}2x + \color{blue}5\)

Our slope will be \(\color{lime}2\).

\(\bf\small Point-Slope~form:\)

\(y - \color{blue}{y_1} = \color{lime}{m}(x -\color{yellow}{ x_1})\)

Where \(\color{lime}m\) = slope, \(\color{blue}{y_1}\) = y-value on the line, and \(\color{yellow}{x_1}\) = x-value on the line.

So if we have:

\(y - \color{blue}5 = \color{lime}5(x - \color{red}2)\)

Our slope will be \(\color{blue}5\).

But some equations like:

\(\bf\small Standard~form:\)

\(Ax + By = C\)

To find the slope of the equation, we have to rearrange it into slope-intercept form(\(y = \color{lime}mx + \color{blue}b\)).

So if we have:

\(2x + 3y = 6\)

First, we subtract 2x to both sides:

\(3y = -2x + 6\)

Now we divide 3 to all terms:

\(y = \color{lime}{-\dfrac{2}{3}}x + \color{blue}2\)

Now we can see that the slope of the equation is \(\color{lime}{-\dfrac{2}{3}}\), and the y-intercept is \(\color{blue}2\).

\(\bf Graph:\)

Slope is also defined as: \(\dfrac{Rise}{Run}\). We can see this on graphs of lines.

\(\bf\small Rise:\)

Rise represents the numerator of the slope(ex: In \(m = \dfrac{1}{2}\) 1 is the rise).

Rise can be either going up or down, where up brings a positive number and down brings a negative.

\(\bf\small Run:\)

Run represents the denominator of the slope(ex: In \(m = -\dfrac{4}{5}\) -5 is the run).

Graph example:

http://img.sparknotes.com/figures/3/393a0f9064f0cef5c349ab5966e8842d/slope.gif

We can see that the rise here is \(4\), and the run is \(2\), that means the slope will be \(\dfrac{4}{2}\) which simplifies to \(2\).

\(\bf Formula:\)

The formula for slope is \(m = \dfrac{y_2-y_1}{x_2-x_1}\).

This formula is mostly used to find the slope between two points(ex: (2, 3) and (5, 8)). But it can also be used to find the slope on a graph, where we can just take two points from that graph and plug them in.

If we are given:

\((\color{red}5,\color{lime} 6)\) and \((\color{yellow}8, \color{blue}{12})\)
^ ^ = \(\color{lime}{y_1}\) ^ ^ = \(\color{blue}{y_2}\)
| = \(\color{red}{x_1}\) | = \(\color{yellow}{x_2}\)

Plug them into the slope equation:

\(m = \dfrac{\color{blue}{y_2}-\color{lime}{y_1}}{\color{yellow}{x_2}-\color{red}{x_1}}\)

\(m = \dfrac{\color{blue}{12}-\color{lime}6}{\color{yellow}8-\color{red}5}\)

Subtract the terms in the numerator and the denominator:

\(m = \dfrac{6}{3}\)

Simplify by dividing:

\(m = 2\)

Therefore the slope between \((5, 6)\) and \((8, 12)\) is \(\color{red}2\).

Answer 2

It should be:

"Our slope should be \(\color{lime}5\)." not "Our slope should be \(\color{blue}5\)."

Answer 3

I made this because SO many people ask questions about Slope.

Answer 4

Congratulations @iGreen for making this tutorial. There are so many people that need help on slope. I am sure many people will appreciate your hard work.

Answer 5

Thanks @confluxepic , :)

Answer 6

I would use darkgoldrenrod, or just goldenrod as a color instead of yellow, because it is not so well seen, but a GREAT TUTORIAL.

I like it:)

Answer 7

@iGreen Those lazy people just want ansurs,Others attend their school lectures attentively..but yes this may help a lot of people. Good job. :)

Answer 8

Thanks! @SolomonZelman It means a lot, you've helped me a lot in the past.

Thanks for the tip too.

Answer 9

Yep, that's true. @uri

Answer 10

yw...

Answer 11

Neat work !
Keep it up

Answer 12

Thanks, @Abhisar

Answer 13

@iGreen Ironically, I was just going over slope in algebra this past week. My teachers just couldn't get me to understand. This tutorial has helped me. Thanks!!!!

Answer 14

No problem! I'm glad it helped!