Ask a New Question
Menu

The graphed line shown below is y = 5 x minus 10.

On a coordinate plane, a line goes through (2, 0) and (3, 5).

Which equation, when graphed with the given equation, will form a system that has no solution?
y = negative 5 x + 10
y = 5 (x + 2)
y = 5 (x minus 2)
y = negative 5 x minus 10

1 answer

For a system of equations to have no solution, the two lines must be parallel. This means they must have the same slope but different y-intercepts.

Given the equation \( y = 5x - 10 \), the slope is 5.

Let's analyze the provided options:

  1. \( y = -5x + 10 \): This has a slope of -5. It is not parallel to \( y = 5x - 10 \).

  2. \( y = 5(x + 2) \): This can be rewritten as \( y = 5x + 10 \). The slope is 5, but the y-intercept is different (10 instead of -10), making it parallel to the original equation.

  3. \( y = 5(x - 2) \): This can be rewritten as \( y = 5x - 10 \). This is the same line as the original equation, so they would overlap and have infinitely many solutions.

  4. \( y = -5x - 10 \): This has a slope of -5, so it is not parallel to \( y = 5x - 10 \).

The equation that will form a system with no solution is:

\( y = 5(x + 2) \) (or \( y = 5x + 10 \)).