How to make sense of graphing relationships? Let x be an apple (x = apple).
Let y be an orange (y = orange).
let 3x = 2y be a proportional relationship. That is, having 3 apples is the equivalent as having 2 oranges.
Now lets graph our relationship:
Y
9           1
8
7
6       1
5
4
3   1
2
1
0 1 2 3 4 5 6 7 8 9 X

The question is, if I am saying that x + x + x = y + y, then why the graph is showing 2 apples in the apple dimension and 3 oranges in the orange dimension. It sounds like the opposite of what I am trying to say.
Instead, I was expecting 3 apples in the apple dimension and 2 oranges in the orange dimension:
Y
9
8
7
6                 1
5
4           1
3
2     1
1
0 1 2 3 4 5 6 7 8 9 X

Why this looks counter intuitive?
 A: If

3 dollars = 2 euros

then the proportionality constant is
$$
\frac{3}{2}\frac{\text{dollars}}{\text{euro}} 
$$
which is just another way to write the number $1$.
Then the relationship is
$$
\text{quantity of dollars} =  
\frac{3}{2} \frac{\text{dollars}}{\text{euro}} 
\times \text{quantity of euros}.
$$
If you draw the graph with quantity of euros on the $x$-axis and quantity of dollars on the $y$-axis the line will have slope $3/2$ and go through the point $(2,3)$.
A: Your equation 3x=2y is wrong, if x is the number of apples, put in x=3  and you know y=2 so you would have $3*3=2*2$ and you see it is wrong.
the relation of number of apples to number of oranges x/y=3/2 and so you have 2x=3y your second graph saying "let x be an apple" is misleading , say x is the number of apples  ans always try you equation with numbers you know.
A: You are misinterpreting what $3x=2y$ means. If x=(number of apples) and y=(number of oranges), then $3x=2y$ does not means that 3 apples are equivalent to 2 oranges. This tells you that 3 times the number of apples is equal to 2 times the number of oranges. So, if you have 3 apples, you have $3\cdot3=9$ which is 2 times the number of oranges, so the oranges are $\frac{9}{2}$, so you have 4 and a half oranges.
In order to visualize it graphically, it is better to isolate the $y$ dividing both sides by its coefficient, so the equation becomes:
$$y=\frac{3}{2}x \ , $$
which means that for each apple (x) you have $\frac{3}{2}$ oranges, i.e. one orange and a half.
