determine which two represent perpendicular lines; y=6x-3,y=1/6x+3, y=-1/6+3, or y=1/6x-3.
To be perpendicular, one equation must have a slope that is the negative of the reciprocal of the other. The slope of the first one is 6, the second is 1/6, the third is -1/6, the fourth is 1/6.
To determine which two lines represent perpendicular lines, we need to compare their slopes. Perpendicular lines have slopes that are negative reciprocals of each other.
The equation y=6x-3 is in the form y=mx+b, where m represents the slope of the line. In this case, the slope is 6.
The equation y=1/6x+3 has a slope of 1/6, which is the reciprocal of 6. However, it is not negative, so it is not perpendicular to the first line.
The equation y=-1/6x+3 also has a slope of -1/6, which is the negative reciprocal of 6. However, it is not perpendicular to the first line either, as it has the same slope.
The equation y=1/6x-3 has a slope of 1/6, which is the reciprocal of -6. In this case, the slope is negative, so it is perpendicular to the first line.
Therefore, the two lines that represent perpendicular lines are y=6x-3 and y=1/6x-3.