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 = negative 4 (x + 1) B) y = negative (x + 4) C) y = negative one-half (2 x minus 8) D) y = x + negative 4

C

Step-by-step explanation:

We need to form a system of equations with an infinite number of solutions. The only way to satisfy this is to find an equation exactly the same as the first equation.

An equation with the same slope but different y-intercept would have 0 solutions.

An equation with a different slope and y-intercept would result in 1 solution.

Let's simplify the given options to find the right choice.

A) y=-4(x+1)

Distribute

y=-4x-4

B) y=-(x+4)

Distribute

y=-x-4

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

Distribute

y=-x+4

D) y=x+-4

y=x-4

Therefore, the correct choice is C, as it is the only equation identical to the original equation.

the answer is a if my teacher taught me correct

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true