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.
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
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.
Since the line passes throught the origin, and the slope builds an angle between 45 and 90 degrees, I can say that: [tex] y - x = a ( y + x), \ a > 1 [/tex] Solve this for y. What do you get?
Solve for y. Plug-in some positive numbers greater than 1, for a. BTW: Mentallic is right about what's the correct answer .
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.