The graph for the equation y = negative 2 x + 1 is shown below.

On a coordinate plane, a line with negative slope goes through (0, 1) and (1, negative 1).

If another equation is graphed so that the system has no solution, which equation could that be?
y = negative 2 (x minus one-half)
y = negative one-half (4 x + 2)
y = negative x + 1
y = negative one-half x + 2

  y = -1/2 (4 x + 2)

Step-by-step explanation:

A system of two equations with no solution will consist of equations for parallel lines. The line will be parallel if they have the same slope (x-coefficient) and different y-intercepts.

The given line has a slope of -2, so eliminating the last two choices.

The first two choices can be expanded to slope-intercept form:

  y = negative 2 (x minus one-half)  ⇒  y = -2x +1 . . . same as given line

  y = negative one-half (4 x + 2)  ⇒  y = -2x -1 . . . parallel line

There will be no solution if another equation is ...

  y = -1/2(4x +2)