Question

NEED ANSWER ASAP

Graph the functions f(x)=−2x−6 and g(x)=−2x−6 on the same coordinate plane. What are the solutions of the equation −2x−6=−2x−6? Select each correct answer. Responses x=−1 x equals negative 1 x = 0 x, = 0 x = 1 x, = 1 x = 2 x, = 2 x = 3

Answer 1

The two functions f(x)=-2x-6 and g(x)=-2x-6 represent the same line on the coordinate plane, since they have the same slope (-2) and y-intercept (-6). Therefore, when we solve the equation -2x-6=-2x-6, we get infinitely many solutions that satisfy the equation, since any value of x will make both sides of the equation equal.

So, the correct answers are:
- x = -1 (since -2(-1)-6 = -2(-1)-6 = -4-6 = -10)
- x = 0 (since -2(0)-6 = -2(0)-6 = -6)
- x = 1 (since -2(1)-6 = -2(1)-6 = -2-6 = -8)
- x = 2 (since -2(2)-6 = -2(2)-6 = -4-6 = -10)
- x = 3 (since -2(3)-6 = -2(3)-6 = -6-6 = -12)

Therefore, the correct answers are x = -1, x = 0, x = 1, x = 2, and x = 3.

Answer 2

The equation possesses an infinite solution set, encompassing all real numbers. Examining specific values, the equation is satisfied for x = -1, x = 0, x = 1, x = 2, and x = 3, affirming the consistent equality of both sides.

The functions f(x) = -2x - 6 and g(x) = -2x - 6 represent the same line on the coordinate plane, sharing identical slopes (-2) and y-intercepts (-6). The equation -2x - 6 = -2x - 6 emerges from equating these functions. This equation simplifies to 0 = 0, indicating that every real number x is a solution since both sides are perpetually equal.

Graphically, the functions overlap entirely, forming a single line extending infinitely along the x-axis. The shared equation demonstrates that any value for x results in a valid solution. Specifically, when evaluating the equation, x can be -1, 0, 1, 2, 3, or any other real number, showcasing the infinite nature of solutions.