Question

The graph is shown for the equation y = –x + 4.

Which equation, when graphed with the given equation, will form a system that has an infinite number of solutions?

A. y = -4(x+1)
B. y = -(x+4)
C. y = -1/2(2x-8)
D. y = x + -4

Answer 1

C. y=-1/2(2x-8)

Explanation:

Your welcome :)

Answer 2

Option C.
`y=-(1)/(2)(2x-8)`

Explanation:

we know that

If a system of two linear equations has an infinite number of solutions, then both equations must be identical

The given equation is

`y=-x+4`

Verify each case

Option A. we have

`y=-4(x+1)`

apply distributive property

`y=-4x-4`

Compare with the given equation

`-x+4 \\eq -4x-4`

Option B. we have

`y=-(x+4)`

remove the parenthesis

`y=-x-4`

Compare with the given equation

`-x+4 \\eq -x-4`

Option C. we have

`y=-(1)/(2)(2x-8)`

apply distributive property

`y=-x+4`

Compare with the given equation

`-x+4=-x+4`

therefore

This equation with the given equation form a system that has an infinite number of solutions

Option D. we have

`y=x+4`

Compare with the given equation

`-x+4 \\eq x+4`