Question

The graphed line is y=-4x-12. Which equation, when graphed with it, will form a system with no solution?

a) y=4x+12
b) y=-4x
c) y=-12
d) y=-4(x+3)

Answer 1

To form a system with no solution, we need an equation that represents a line that is parallel to the given line but does not intersect it. The equation y=-12 (option c) represents a horizontal line with no slope that will not intersect the given line.

Step-by-step explanation:

The equation y=-4x-12 represents a line with a negative slope and y-intercept of -12. To form a system with no solution, we need an equation that represents a line that is parallel to the given line but does not intersect it. The equation y=4x+12 (option a) represents a line with the same slope but a different y-intercept than the given line, so it will intersect the given line at a point. The equation y=-4x (option b) represents a line with the same slope but no y-intercept, so it will intersect the given line at the x-axis. The equation y=-12 (option c) represents a horizontal line with no slope that will not intersect the given line. Therefore, option c is the correct answer.