Question

The graphed line shown below is y = negative 3 x + 6.

On a coordinate plane, a line goes through points (1, 3) and (2, 0).

Which equation, when graphed with the given equation, will form a system that has no solution?
y = 3 x + 6
y = negative 3 (x + 6)
y = negative 3 (x minus 2)
y = 3 (x minus 2)

Answer 1

The equation y = -3(x + 6) will form a system that has no solution when graphed with the equation y = -3x + 6 as it represents a parallel line with a different y-intercept (-18).

Step-by-step explanation:

To determine which equation will form a system that has no solution when graphed with the given equation y = -3x + 6, we need to find an equation that represents a line parallel to the given line.

Two lines are parallel if they have the same slope but different y-intercepts. The given line has a slope of -3.

Therefore, to have no solution, the new line must also have a slope of -3 but a different y-intercept from 6.

The equations are:

• y = 3x + 6: This line has a slope of 3, which is not parallel to the given line (opposite slope).
• y = -3(x + 6): Simplifying this, y = -3x - 18, which is parallel to the given line and has a different y-intercept (-18).
• y = -3(x - 2): Simplifying this, y = -3x + 6, which is the same line as the given equation.
• y = 3(x - 2): This line has a slope of 3, which is not parallel to the given line.

Therefore, the equation y = -3(x + 6) will form a system that has no solution when graphed with the equation y = -3x + 6 because it is parallel and has a different y-intercept.