Determine which two equations represent perpendicular lines.
a) y=2x - 6
b) y=1/2x + 6
c) y= -1/2x + 6
d) y= 1/2x - 6
I know that perpendicular lines have negative recipricals, but I'm having trouble with this problem. I think the answer is b & c because they are both 1/2 and they have the (+6) and not (-6). I'm really confused though, because 1/2 and -1/2 aren't really negative recipricals because its the same number. I was thinking it should be 2 and -1/2.(which would make it perpendicular) I'm lost! does the plus 6 and minus 6 matter??
The SLOPES of perpendicular lines are negative reciprocals. That means the product of the two slopes is -1. Clearly, this applies to (a) and (c), for which the slopes are 2 and -1/2.
To determine which two equations represent perpendicular lines, you need to compare the slopes of the lines. Remember that the slope-intercept form of a line is y = mx + b, where m is the slope.
The perpendicular lines have slopes that are negative reciprocals of each other. The negative reciprocal of a number is found by taking its reciprocal (flipping it upside down) and then changing the sign.
Let's analyze each equation:
a) y = 2x - 6
The slope of this line is 2.
b) y = (1/2)x + 6
The slope of this line is 1/2.
c) y = -1/2x + 6
The slope of this line is -1/2.
d) y = (1/2)x - 6
The slope of this line is 1/2.
To determine which equations represent perpendicular lines, we need to find pairs of lines with slopes that are negative reciprocals.
Comparing the slopes, we can see that the lines with equations (a) and (c) have slopes that are negative reciprocals of each other. The slope of line (a) is 2, and the slope of line (c) is -1/2.
Therefore, the equations that represent perpendicular lines are:
a) y = 2x - 6
c) y = -1/2x + 6