Determine if the equations represent parallel lines, perpendicular lines, or neither.
l1:y=3x+4
l2:y=-1/3x-1
The equations l1: y = 3x + 4 and l2: y = -1/3x - 1 represent neither parallel lines nor perpendicular lines.
To determine if the equations represent parallel lines, perpendicular lines, or neither, we need to compare their slopes.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope.
For line l1: y = 3x + 4
The slope of line l1 is 3.
For line l2: y = (-1/3)x - 1
The slope of line l2 is -1/3.
Parallel lines have the same slope, so if the slopes of l1 and l2 are equal, the lines are parallel.
Perpendicular lines have slopes that are negative reciprocals of each other, so if the product of the slopes is -1, the lines are perpendicular.
Let's calculate the product of the slopes:
(3) * (-1/3) = -1.
Since the product of the slopes is -1, the lines l1 and l2 are perpendicular.
To determine if two lines are parallel, perpendicular, or neither, we can compare their slopes.
In the given equations:
l1: y = 3x + 4
l2: y = -(1/3)x - 1
We can see that the equations are both in slope-intercept form, y = mx + b, where "m" represents the slope of the line.
The slope of l1 is 3, and the slope of l2 is -(1/3).
If two lines have equal slopes, they are parallel.
If the slopes of two lines multiply to give -1, they are perpendicular.
Let's compare the slopes:
Slope of l1 = 3
Slope of l2 = -(1/3)
Since the slopes are not equal, and their product is not -1, we can conclude that the lines l1 and l2 are neither parallel nor perpendicular.