Question

Tutorial: Slope

Answer 1

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

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

Positive slope rises from LEFT to RIGHT.

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

Negative slope declines from LEFT to RIGHT.

Examples of Positive and Negative Slopes:

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

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

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

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

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

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

There are 3 different ways to find slope.

\(\sf Equations: \)

Some equations just give you the slope, for example:

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

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

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

So if we have:

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

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

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

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

Where \(\sf\color{lime}m\) = slope, and \(\sf ( \color{yellow}{x_1} , \color{blue}{y_1})\) is a point on the line.

So if we have:

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

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

But some equations like:

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

\(\sf Ax + By = C \)

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

So if we have: \(\sf 2x + 3y = 6 \)

First, we subtract 2x to both sides:

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

Now we divide 3 to all terms:

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

Now we can see that the slope of the equation is \(\sf\color{lime}{-\dfrac{2}{3}}\).

\(\sf Graph: \)

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

\(\sf\small Rise: \)

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

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

\(\sf\small Run: \)

Run represents the denominator of the slope(ex: In \(\sf m = -\dfrac{4}{5}\), -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 \(\sf\dfrac{4}{2}\) which simplifies to 2.

\(\sf Formula: \)

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

This formula is mostly used to find the slope between two points(ex: \(\sf (2, 3)\) and \(\sf (5, 8)\)). 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:

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

Plug them into the slope equation:

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

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

Subtract the terms in the numerator and the denominator:

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

Simplify by dividing:

\(\sf m = 2 \)

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

Answer 2

Good Job

Answer 3

Nice~

Answer 4

thanks

Answer 5

Tank chu

Answer 6

thank you

Answer 7

Gracias

Answer 8

ty