Determine if the equations represent parallel lines, perpendicular lines, or neither.
l1:y=2/9x+4
l2:y=-9/2x+3
The equations represent perpendicular lines because the slopes of the two lines are negative reciprocals of each other. The slope of line 1 is 2/9 and the slope of line 2 is -9/2, which are negative reciprocals (-9/2 * 2/9 = -1).
To determine if the equations represent parallel lines, perpendicular lines, or neither, we will compare the slopes of the lines.
The slope-intercept form of a linear equation is y = mx + b, where m represents the slope.
For l1: y = (2/9)x + 4, the slope is 2/9.
For l2: y = (-9/2)x + 3, the slope is -9/2.
Two lines are parallel if their slopes are equal. In this case, the slopes are not equal, so l1 and l2 are not parallel lines.
Two lines are perpendicular if the product of their slopes is -1. So, we can check if (2/9) * (-9/2) = -1. Simplifying the multiplication on the left side, we get -18/18, which is equal to -1.
Since the slopes multiply to -1, l1 and l2 are perpendicular lines.
Therefore, the equations represent perpendicular lines.
To determine if the equations represent parallel lines, perpendicular lines, or neither, we can compare their slopes.
For the first equation, l1: y = (2/9)x + 4, the slope is 2/9.
For the second equation, l2: y = (-9/2)x + 3, the slope is -9/2.
If two lines have slopes that are equal, the lines are parallel. If two lines have slopes that are negative reciprocals of each other (the product of their slopes is -1), the lines are perpendicular.
Let's check the slopes:
Slope of l1: 2/9
Slope of l2: -9/2
Since the slopes of l1 and l2 are NOT equal, and their product is NOT -1, we can conclude that the lines l1 and l2 are neither parallel lines nor perpendicular lines.