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Does the slope depend on how the y of a straight line changes or on both x and y?

For example, A straight line 2x - y = 0 passing through origin has a slope m = 2.

Now, when

x = 1  |  y = 2 x = 2  |  y = 4 x = 3  |  y = 6 

It looks like the value of y is increasing by 2, which is confusing me because m = 2.

In case 2, A straight line 2x + 3y = 18 has slope m = -2/3

and, when

x = 1 | y = 5.33 x = 2 | y = 4.66 x = 3 | y = 4 

In this case it looks like the y is decreasing by -2/3

so, does the slopes of a straight line only effect y?

2 Answers 2

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The slope of the straight line is only affecting y in your case because you are deciding to measure y and not x, i.e. you are setting the values of x and calculating the values of y from there.

If you were to draw y = 2x while measuring y (that is, you are setting the values of y and calculating the values of x) you would find that x increases by 1/2 (i.e. 1/m).

y = 1 | x = 0.5 y = 2 | x = 1.0 y = 3 | x = 1.5 

So in actuality m effects whichever value you are calculating, as you are setting the other value yourself (you're affecting the other value)

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The slope of a straight line here is the change in $y$ divided by the change in $x$. Your equation can be written as $y = 2x$ and, as your numbers show, each increase of $x$ by 1 leads to an increase in $y$ by 2.

Draw the lines $y = 2x$ and $y = x$ on co-ordinate axes with the $x$-axis horizontal and $y$-axis vertical, and you will see that the line with a larger slope is steeper.

Added later: On your second added question, you have correctly worked out the slope as close to $-2/3$. But this is not just the change in $y$. If you had only the data

x = 1 | y = 5.33 x = 3 | y = 4     

then the change in $y$ would be $-1.33$, but the change in $x$ would be $2$. You have to divide one by the other. So the slope would be $-1.33/2 \approx -2/3$, as before.