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

Option C.

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

Verify each case

Option A. we have

apply distributive property

Compare with the given equation

Option B. we have

remove the parenthesis

Compare with the given equation

Option C. we have

apply distributive property

Compare with the given equation

therefore

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

Option D. we have

Compare with the given equation

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

d is the correct answer

step-by-step explanation:

x= 8 because 3x = 3 * 8, and 3*8 = 24