# Hard graph !

1. ### ABC_123

5

I know the answer is (E) , but HOW ?

2. ### Mentallic

3,699
Are you sure it's meant to be E) because I'm getting D)

If you were given a linear graph with the vertical axis being Y, and the horizontal being X, then you could say that Y=mX for some constant m, right?

You can similarly substitute each axis representation into this equation. The vertical is now y-x and the horizontal x+y so let Y=y-x and X=x+y and then rearrange the equation to make y the subject.

3. ### ABC_123

5
Sorry,I'm not sure that the correct answer is (E) :(

4. ### Mentallic

3,699
No worries. On the other hand, I'm quite sure the answer is D, but it doesn't even matter, we should just let the math do the talking

5. ### HallsofIvy

40,502
Staff Emeritus
The first graph is a straight line passing through the origin so it must be of the form y- x= k(x+ y). That is the same as y- x= kx+ ky or y- ky= x+ kx. Factoring, (1-k)y= (1+k)x or y= (1+k)/(1-k) x. From the picture it appears that k is larger than 1 (the angle is greater than 45 degrees) so 1-k is negative. That, in turn, means that the fraction (1+k)/(1-k) is negative so the graph goes downward to the right. It also follows that k< -1.

6. ### ABC_123

5
I didn't understand !
:(

Can you explain it more simply ?

7. ### Mentallic

3,699
Can you follow the procedure I outlined for you in post #2?

8. ### Dickfore

Since the line passes throught the origin, and the slope builds an angle between 45 and 90 degrees, I can say that:
$$y - x = a ( y + x), \ a > 1$$

Solve this for y. What do you get?

9. ### ABC_123

5

y(1-a)= x(1+a)

so .. ?

10. ### SammyS

8,431
Staff Emeritus
Solve for y.

Plug-in some positive numbers greater than 1, for a.

### Staff: Mentor

That graph in the picture appears to have a slope of about 3, for each mm horizontally it rises about 3mm, roughly (and assuming the scales are the same).

Usually we would express that graph as being the plot: y = 3x

But on this particular graph, the vertical quantity is given as y-x
and the variable on the horizontal is given as y+x
So substitute these expressions for the y and x in the blue equation, respectively.

Finally, rearrange the result to get y on one side by itself.

12. ### Redbelly98

12,039
Staff Emeritus