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# Positive & negative slope

Sal analyzes what it means for a slope to be positive or negative (spoiler: it affects the direction of the line!).

## Want to join the conversation?

• If let's say you get a slope and it tells you that you need to describe the slope using words like Increasing, Decreasing, Horizontal and Vertical. how would you be able to define those words? •   Increasing: the graph goes up from left to right

Decreasing: the graph goes down from left to right

Horizontal: the graph is perfectly flat (Δy = 0)

Vertical: the graph is perfectly straight up-and-down (Δx = 0)

Hope this helps!
• Why don't you do the slope as ∆x/∆y? Isn't that the same as the coordinates of a coordinate plane? Why do we have to do the slope as ∆y/∆x? I am very confused!!
(1 vote) •  It's because we describe 𝑦 as a function of 𝑥:
𝑦 = 𝑚𝑥 + 𝑏

If we have two points (𝑥₁, 𝑦₁) and (𝑥₂, 𝑦₂) we get the two equations
𝑦₁ = 𝑚𝑥₁ + 𝑏
𝑦₂ = 𝑚𝑥₂ + 𝑏

Thereby,
𝛥𝑦 = 𝑦₂ − 𝑦₁ =
= 𝑚𝑥₂ + 𝑏 − (𝑚𝑥₁ + 𝑏) =
= 𝑚𝑥₂ − 𝑚𝑥₁ = 𝑚(𝑥₂ − 𝑥₁) =
= 𝑚 ∙ 𝛥𝑥 ⇒

⇒ 𝑚 = 𝛥𝑦∕𝛥𝑥
• Does the slope line only have to be in the NE direction? Or can it be in the opposite direction, like NW? • Great Question!

No linear equation slope runs towards Northwest…
but Negatives run from the Northwest to the Southeast, (downward to the right).

±Slopes of a linear equation can be measured in either direction, but the direction the line runs is from Left to Right.

So either towards the Northeast or the Southeast.

Positive slopes have an increasing slope that runs from lower left positions to upper right coordinates.
(always kinda Northeast -ish).
↗️ Positive Slope
is an 'increasing slope' because as x inputs become larger, the y outputs become larger too.

Negative slopes have a decreasing slope, so they run from upper left positions towards lower right coordinates.
(always kinda Southeast -ish).
↘️ Negative Slope
is a 'decreasing slope' because as x inputs become larger, the y outputs become smaller.

Both ↗️↘️ Positive and Negative sloped lines include all x and all y values. So every single number is on their lines!

There's also:
Zero Slope ↔️ a Horizontal Line, that includes all x-values, but only one y-value. As x increases or decreases y just stays the same. (So all possible x inputs map to the same y output.)
Undefined Slope ↕️ a Vertical Line with only one x-value, to all y-values. Vertical line is the only one that doesn't work within a function, since an input must be unique to an output, but one x maps to all y).

★So with Linear Equations, it's just those four slope line types to learn and understand.

Most of the time it will be about…
↗️Positive = increasing y outputs.
↘️Negative = decreasing y outputs.

(≧▽≦) I hope that helps!
• Did you purposefully make lines 1, 2, and 4 (pink, blue, and orange) converge on the same point? • What if you don't have a whole graph and you just have one box how do you figure out if it's negative or positive? • can you get a slope with a decimal point in it • Yes. Say it costs \$4.65 per bag of chips at a store. You can form an equation, y=4.65x to tell you costs for x amount of chips.
You have to realize that you will see these decimals will be turned fractions more often than not because slope is a ratio of change in y/change in x. For money problems as above and some others, they are called unit rate ( \$4.65/1 bag) which are the ones most likely to be decimals.
• why do we use slope man to tell witch slope is positive and witch is negative. is it based on witch way he runs? • slope person is a graphic organizer to help remember, and as will all graphic organizers and mnemonic devices, we use them until we no longer need them any more because we know it. Positive slopes are based on as x increases, y is also increasing, so change in y/change in x is positive. Negative slopes are based on as x increases, y is decreasing, so we end up with a negative change in y/positive change in x which gives a negative answer.   