Hello there. To solve this question, we have to remember some properties about ordered pairs and equations.
Given the equation:
[tex]y=2x-4[/tex]We want to determine the ordered pair that is solution to this equation.
First, remember what is an ordered pair:
An ordered pair is a 2 element tuple (list) that has its elements disposed as
[tex](x,\text{ }y)[/tex]In this case, all solutions x to this equation will be given as the following ordered pairs:
[tex](x,\,2x-4)[/tex]And these points lies on the line y = 2x - 4, all across the xy-plane.
Okay. Now, we have to check which of the options are correct.
For this, you take the first coordinate of the ordered pair and plug in the equation:
a) (4, 5)
Plugging x = 4, we get
[tex]y=2\cdot4-4=8-4=4[/tex]This is not the correct option.
b) (-3, -7)
Plugging x = -3, we get
[tex]y=2\cdot(-3)-4=-6-4=-10[/tex]Not correct as well.
In the end, we find that the only correct option is:
e) (0, -4).
Since plugging x = 0 yields:
[tex]y=2\cdot0-4=-4[/tex]As we wanted.
Therefore the final answer is contained in the last option, (0, -4).
