Determine if the equations represent parallel lines, perpendicular lines, or neither.
L1: y=5x+4
L2: y=-1/5x-1/3
To determine if the equations represent parallel lines, perpendicular lines, or neither, we need to compare the slopes of the lines.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope.
For L1: y = 5x + 4, the slope is 5.
For L2: y = -(1/5)x - (1/3), the slope is -(1/5).
Parallel lines have the same slope. Perpendicular lines have slopes that are negative reciprocals of each other.
Comparing the slopes of L1 and L2, we see that 5 and -(1/5) are negative reciprocals of each other. Therefore, the two lines are perpendicular.
To determine if the equations represent parallel lines, perpendicular lines, or neither, we can compare their slopes.
The slope-intercept form of a line is y = mx + b, where m represents the slope of the line.
For L1: y = 5x + 4
The slope of L1 is 5.
For L2: y = -1/5x - 1/3
The slope of L2 is -1/5.
Since the slopes of L1 and L2 are not equal, the lines are not parallel.
To determine if the lines are perpendicular, we can check if the product of their slopes is -1.
The product of the slopes of L1 and L2 is (5) * (-1/5) = -1.
Since the product of the slopes is -1, the lines L1 and L2 are perpendicular.
Therefore, the equations represent perpendicular lines.
To determine if two lines are parallel, perpendicular, or neither, we need to compare their slopes.
In general, two lines are parallel if and only if their slopes are equal. Two lines are perpendicular if and only if the product of their slopes is -1.
Let's find the slopes of L1 and L2:
L1: y = 5x + 4
In this equation, the slope is 5. It is the coefficient of x.
L2: y = -1/5x - 1/3
In this equation, the slope is -1/5. Again, it is the coefficient of x.
The slopes of L1 and L2 are 5 and -1/5, respectively.
Now, let's compare the slopes:
Since the slopes of L1 and L2 are not equal but their product is not equal to -1 either, we can conclude that L1 and L2 are neither parallel nor perpendicular.