Answer:
Only Choices A and C are correct.
Step-by-step explanation:
The graph has negative slope and its y-intercept is a positive value, and the equations we are looking for should have these two properties.
Let us look at the choices one by one.
Choice A: [tex]3x+2y=6.[/tex]
We solve for y and get:
[tex]y=-\frac{3}{2}x+3[/tex]
This has negative slope and positive y-intercept, therefore this choice is true.
Choice B: [tex]y=5.[/tex]
This is a horizontal line, therefore this choice cannot be correct.
Choice C: [tex]y=-4x+2.[/tex]
This has negative slope and positive y-intercept, therefore this choice is true.
Choice D: [tex]2x-y=7.[/tex]
Solve for y and get:
[tex]y=2x-7.[/tex]
This has positive slope and negative y-intercept, which are not the characteristics of our graph. Therefore this choice is not correct.
Thus only choices A and C apply.
