# Thread: slope on a simple graph

1. ## slope on a simple graph

i have a given point of (3,2)
i know that the slope is 2 and if i move two up i will have y equals 4
but why should i move 1 to the right?
the slope is 2 so i will move to up but why 1 to the right which leads to (4,4)?

2. ## Re: slope on a simple graph

The slope is the ratio of the vertical change to the horizontal change. When the slope of a line is 2 and (x, y) is on the line, then for any number z the point (x + z, y + 2z) is again on the line. Here the vertical change from (x, y) to (x + z, y + 2z) is 2z and the horizontal change is z.

3. ## Re: slope on a simple graph

why do you move on the x axis
i take it from what you said that the slope indicates to move two up and one to the right
why not just two up considering the slope is a standalone 2?

4. ## Re: slope on a simple graph

Originally Posted by ariel32
why do you move on the x axis
i take it from what you said that the slope indicates to move two up and one to the right
why not just two up considering the slope is a standalone 2?
slope is $\displaystyle \frac{\text{change in }y}{\text{change in }x}$

5. ## Re: slope on a simple graph

If a line is sloped, then to move along the line and stay on it you need to move along both the y- and x-axes. The slope of the line is by definition the ratio of those displacements. If you move strictly up, then you leave the line.

6. ## Re: slope on a simple graph

if i may ask why did you decide to move just 1 on the x axis and while i am at it why did you move 2 up the y axis?

7. ## Re: slope on a simple graph

Originally Posted by ariel32
if i may ask why did you decide to move just 1 on the x axis
I never decided this. I never mentioned the number 1 in my posts.

Originally Posted by ariel32
and while i am at it why did you move 2 up the y axis?
If you move 1 along the x-axis, then, in order to stay on the line, you need to move (the slope) * 1 = 2 * 1 = 2 along the y-axis. This is the definition of slope.

8. ## Re: slope on a simple graph

so if the slope was 4 i would move 1 to the right and 4 up?

9. ## Re: slope on a simple graph

Correct! Or 2 to the right and 8 up and so on.

10. ## Re: slope on a simple graph

i understand more now
i suppose you have to move 1 to the right so that the run principle is met
but why move 2 up and not 1 up?
if you move 1 up you would still have a new point?

11. ## Re: slope on a simple graph

Originally Posted by ariel32
if you move 1 up you would still have a new point?
Yes, but this point would not be on the line.

12. ## Re: slope on a simple graph

ok one final remark on the matter then.
if you say that going 1 to the right means going 2 up by definition i would expect that going 10 to the right would not change the definition of the slope and expect to go only 2 up in such case or is the rule based differently?

13. ## Re: slope on a simple graph

Originally Posted by ariel32
if you say that going 1 to the right means going 2 up by definition i would expect that going 10 to the right would not change the definition of the slope and expect to go only 2 up in such case or is the rule based differently?
Originally Posted by emakarov
The slope is the ratio of the vertical change to the horizontal change. When the slope of a line is 2 and (x, y) is on the line, then for any number z the point (x + z, y + 2z) is again on the line. Here the vertical change from (x, y) to (x + z, y + 2z) is 2z and the horizontal change is z.
If you move z = 10 to the right, then you need to move 2z = 20 up to stay on the line.