How do you tell if the slope is positive or negative?

Question

I know that there are four different kinds of slope, but I get really confused between positive and negative slope. There's undefined slope, positive slope, negative slope, and undefined slope.

Answer 1

I placed a video on my page.

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If the line slants up going left to right on the graph it is positive slope.

If the line slants down going left to right on the graph it is negative slope.

A horizontal line is 0 slope.

A vertical line tells you that the slope does not exist.

To go more in depth:

The Slope Intercept Form is y = mx + b. An example is y = 3x + 5.

If the number before the x (the number being multiplied to the x) is positive, it is positive slope. If the number before the x is negative, it is negative slope. If you have y = 3 or any other number and you do not see an x in the equation, it is a horizontal slope because the number before the x is zero. Sometimes the equation might look like y = 0x + 3. Zero times x is zero so you just have y = 3. This is seen by a horizontal line when graphing. We say that the slope is zero. If you have x = 2 or x is equal to any other number, then you do not have a y in the equation, and we say that the slope does not exist. This is a vertical line.

Answer 2

On a graph of x and y, a positive slope means x and y increase or decrease together. Therefore:

Positive Slope

-As x increases, y increases.

-As x decreases, y decreases.

in slope-intercept form of the equation of a line:

y = mx+b

a positive slope occurs when "m" is positive (m > 0).

On the contrary, a negative slope means x and y increase or decrease opposite of each other. Therefore:

Negative Slope

-As x increases, y decreases

-As x decreases, y increases.

in slope-intercept form of the equation of a line:

y = mx+b

a negative slope occurs when "m" is negative (m < 0).

A slope of zero is a horizontal flat line where no matter the value of x, y = a constant value.

defining slope as

change in y / change in x = (y₂-y₁) / (x₂-x₁)

y₂ = y₁ = 3

slope = (3-3)/(x₂-x₁) = 0

The change in y is zero because y₂ = y₁ = some constant number (here we set y=3). Zero divided by any number is 0.

in slope-intercept form of the equation of a line:

y = mx+b

a zero slope occurs when "m" is 0 (m = 0).

An undefined slope is a vertical line where no matter the value of y, x = a constant value (slope = undefined). This is known as undefined because:

defining slope as

change in y / change in x = (y₂-y₁) / (x₂-x₁)

let's say x₂ = x₁ = 5

undefined slope:

(y₂-y₁) / (5-5) = (y₂-y₁) / 0

The change in x is zero because x₂ = x₁ = some constant number (here we set x =5). Dividing by zero is undefined.

Answer 3

There are 4 kinds of slope, absolutely correct! However, the positive and negative slopes can be told apart verbally as follows:

A line with a POSITIVE slope is going to INCREASE from left to right.

A line with a NEGATIVE slope is going to DECREASE from left to right.