The options are; (0,2) (-4,0), (-4, -2) (0, -2)

Hi Adeline;

2x – 4y = 8

(0,2) (-4,0), (-4, -2) (0, -2)

(0,2) and (0,-2) are y-intercepts, the value of y when x=0.

The equation is currently in standard form...

Ax+By=C, A>0

Let's convert the equation into slope-intercept form..

y=mx+b

m is the slope.

b is the y-intercept.

2x-4y=8

Let's subtract 2x from both sides...

2x-2x-4y=-2x+8

-4y=-2x+8

Let's divide both sides by -4...

(-4y)/-4=(-2x+8)/-4

y=(1/2)x-2

y-intercept is -2, (0,-2)

**We have ruled-in one answer (0,-2)**, and ruled-out the other (0,2).

(-4,0) is the x-intercept, the value of x when y=0.

Let's return to the original equation and plug-in y=0...

2x – 4y = 8

2x-[(4)(0)]=8

2x=8

x=4

This is the wrong result. We have ruled-out another answer, (-4,0).

(-4,-2)

This one has no special features. We will have to plug it into the equation...

2x-4y=8

[(2)(-4)]-[(4)(-2)]=8

-8-(-8)=8

Subtracting a negative number is the same as adding a positive number...

-8+8=8

Does not work.