Question

The graph for the equation y = negative x + 2 is shown below.

On a coordinate plane, a line with positive slope goes through (0, 2) and (2, 0).

If another equation is graphed so that the system has an infinite number of solutions, which equation could that be?
y = negative 2 (x minus 1)
y = negative (x + 2)
y = negative one-fourth (4 x minus 8)
y = negative one-half (x + 4)

Answer 1

The equation y = -2(x - 1) would create an infinite number of solutions when paired with y = -x + 2 since it is a constant multiple and represents the same line (option A).

What is a system of equations with infinite solutions?

For the system to have an infinite number of solutions, the two equations must represent the same line. This occurs when the two equations are proportional, meaning one is a constant multiple of the other.

Among the given options, the equation y = -2(x - 1) can be proportional to y = -x + 2 if you distribute the -2 and simplify:

y = -2x + 2

So, the equation y = -2(x - 1) would create a system with an infinite number of solutions when combined with y = -x + 2.