Question

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

Answer 1

Answer:

Option C. $y=-\frac{1}{2}(2x-8)$

Step-by-step 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

$-x+4 \neq -4x-4$

Option B. we have

$y=-(x+4)$

remove the parenthesis

$y=-x-4$

Compare with the given equation

$-x+4 \neq -x-4$

Option C. we have

$y=-\frac{1}{2}(2x-8)$

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

$-x+4 \neq x+4$