Slope

Key Questions

How does a positive slope differ from a negative slope?

The slope is a number that tells you how much y changes when x changes.
For example: a slope of 5 means that for each change in x of 1 unit (for example between 6 and 7) the correspondig y changes of 5 units.

This is for a positive slope, so that your value of y is getting...bigger!!!

The negative slope is the opposite, it tells you of how much y decreases for each increas of 1 unit in x.
A slope of -5 tells you that the value of y decreases of 5 units in the 1 unit interval of x:

As you may guess the slope is a measure of the "inclination" of your line!!!

Try to guess what a slope of zero means!!!!!!

Gió · 2 · Dec 17 2014
How does change in the slope affect the steepness of a line?

Answer:

See below:

Explanation:

The steepness of a line is essentially the slope. When we see a line oriented from bottom left to upper right, it has a positive slope. A negative slope would be depicted by a line going from the upper left to bottom right.

Slope values increase the higher the number is: For instance, a line with a slope of $2$ is steeper than a line with a slope of $1/2$ .

Hope this helps!

Jacobi J. · 1 · Jun 20 2018
How do you calculate the slope given two points?

Use the slope formula ( $m = (y_2 - y_1)/(x_2 - x_1)$ ) to calculate the slope given two points $(x_1, y_1)$ and $(x_2, y_2)$ .

Here is an example of finding the slope, given two points (-2,3) and (4,-5).

$(-2, 3) = (x_1, y_1)$
$(4, -5) = (x_2, y_2)$

$m = (y_2 - y_1)/(x_2 - x_1)$

$m = (-5 - 3)/(4 - (-2))$

$m = (-5 - 3)/(4 + 2)$

$m = (-8)/(6)$

$m =-4/3$

The slope of of (-2,3) and (-4,5) is $-4/3$

Elizabeth P. · 1 · Nov 16 2014
How do you calculate slope from a graph?

Nuzhat has already discussed how you can find the slope of a line from two points that lie on the line. I'll discuss two other methods of finding the slope from a graph.

1. From the angle made with the x-axis

Since the slope of a line is basically the ratio of the y-component of the line to its x-component,

The slope of a line can be found out by taking tangent of the angle between the given line and the x-axis.

Consider the following figure:

In this case, the angle between the x-axis and the line is $theta$ .

Therefore,
Slope of the given line = $tantheta$

Note: Angles in the counterclockwise direction are taken as positive, and those in the clockwise direction are taken as negative.

For example, if the angle between the x-axis and the given line is $30^o$ ,

Slope of the given line = $tan30=1/sqrt3$

2. From the equation of the line

The slope of a line can also be determined from its equation. The standard form of the equation of a line is:

$Ax^2+By+C=0$

where $A,B and C$ are some constants.

First, the equation of the line must be written in the standard form.

Then, the slope of the line = $-A/B$

For example, let the equation of the given line be $x^2+3=2y$ .

Rewriting in the standard form, we get: $x^2-2y+3=0$
and we can see that:
$A=1$
$B=-2$
$C=3$

Therefore, the slope of the line $=-A/B=-(1)/(-2)=1/2$

Tanish J. · 2 · Nov 28 2014
What is Slope?

Answer:

Slope is the change in the y values divided by the change in the x values

Explanation:

$"slope"="rate of change in y"/"rate of change in x" ="rise"/"run"$

$(color(blue)(x_1),color(blue)(y_1))$

$(color(red)(x_2),color(red)(y_2))$

$color(green)m =(color(red)(y_2)-color(blue)(y_1))/(color(red)(x_2)-color(blue)(x_1))$

Is is often expressed as rise over run.

Bill Jorgensen · 1 · Jun 8 2018