SOLUTION: Can someone please explain to me what a slope actually is? Is it a value? Is it the y-value? if so why the y-value? I know it's defined like m = (y2-y1)/(x2-x1) but that doesn't

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Question 1017914: Can someone please explain to me what a slope actually is? Is it a value? Is it the y-value? if so why the y-value?
I know it's defined like m = (y2-y1)/(x2-x1) but that doesn't make sense to me. Why the change in y's and the changes in x's? I don't get it. And why are they being divided? what does division do to them? Why does subtracting the y or x values give us their overall change? Is y the change in height and x the change in length? Or should I think of it like vertical distance / horizontal distance?
I think I understand parts of slope, like slope can be thought of like an angle and at what angle it is shows how much it rises or falls over a certain region, I think? like a gradual increase or decrease?
This is such a confuses concept for me. How can slope be a value? like how does that even work?

Thank you



Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Can someone please explain to me what a slope actually is? Is it a value? Is it the y-value? if so why the y-value?
I know it's defined like m = (y2-y1)/(x2-x1) but that doesn't make sense to me. Why the change in y's and the changes in x's? I don't get it. And why are they being divided? what does division do to them? Why does subtracting the y or x values give us their overall change? Is y the change in height and x the change in length? Or should I think of it like vertical distance / horizontal distance?
I think I understand parts of slope, like slope can be thought of like an angle and at what angle it is shows how much it rises or falls over a certain region, I think? like a gradual increase or decrease?
This is such a confuses concept for me. How can slope be a value? like how does that even work?
========================
Or should I think of it like vertical distance / horizontal distance?
That's what it is. It's the vertical change divided by the horizontal change.
========================
This is such a confuses concept for me. How can slope be a value? like how does that even work?
eg, the vertical change is 1 foot.
The horizontal is 10 feet.
slope = 1/10
What's wrong with that being a value?
================
Slope is an indication of "steepness."
If a road changes in elevation by 5' in 100' horizontal, it's not as steep as a road that change 10' V in 100' H.
---------
The slope of a ski jump is greater than the "bunny hills."


Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Can someone please explain to me what a slope actually is?
Is it a value?                     Yes

Is it the y-value?                 Not applicable

if so why the y-value?             Not applicable

I know it's defined like m = (y2-y1)/(x2-x1)      correct; good

but that doesn't make sense to me.                bad

 Why the change in y's and the changes in x's?    by the definition

I don't get it.                                   bad

And why are they being divided?                   by the definition

what does division do to them?                    It produces the value of the slope

Why does subtracting the y or x values give us their overall change?    It is obvious

Is y the change in height and x the change in length?                   You may interpret it like this

Or should I think of it like vertical distance / horizontal distance?   You may interpret it like this, too

I think I understand parts of slope, like slope 
can be thought of like an angle and at what angle 
it is shows how much it rises or falls over a certain region,           It is close, but the slope is not an angle. It is the tangent of the angle

I think? like a gradual increase or decrease?   It is correct

This is such a confuses concept for me.         It is so clear
How can slope be a value?                       By the definition
like how does that even work?                   Imagine the plot of a  distance as the function of time. Then the slope is the average speed.


Thank you                                       Please


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