Which complex number's graph is shown?

Option D.

Step-by-step explanation:

When we want to graph a complex number in a coordinate axis, the real part of the complex number is represented by the x-axis, and the complex part is represented by the y-axis.

in this case, we can see that the coordinates of the point are:

(-2, 2)

Then the complex number is:

Z = -2 + 2*i

Now we need to see which one of the given options is equal to this.

Let's check the real part for every option, so we can discard some of them:

A) real part = -2*cos(135°) = 1.41  (we can discard this option)

B) real part = 2*cos(7*pi/4) = 1.41 (we can discard this option)

C) real part = √2*2*cos(225°) = -2

D) real part = √2*2*cos(3*pi/4) = -2  

So options C or D are the correct one, now let's check the complex part for each one

C) complex part = √2*2*sin(225°) = -2    (we can discard this option)

D) complex part =  √2*2*sin(3*pi/4) = 2

So the correct one is the D option.

a) y = -3x +2

b) y = 1/2x -6

these 2 can be combined into one equation.

-3x +2 = .5x -6

8 = 3.5x

x = 8 / 3.5 = 2.2857142857

y = -3 * (8 / 3.5) +2

y = (-24 / 3.5) + 2

y = -4.8571428571

step-by-step explanation: