Determine if the equations represent parallel lines, perpendicular lines, or neither.
l1:y=6/5x-2/3
l2:y=-5/6x-1
To determine if the equations represent parallel lines, perpendicular lines, or neither, we need to look at the slopes of the lines.
The slope of a line can be determined by the coefficient of x in the equation. In the first equation, y = (6/5)x - (2/3), the coefficient of x is 6/5, so the slope of line l1 is 6/5.
In the second equation, y = (-5/6)x - 1, the coefficient of x is -5/6, so the slope of line l2 is -5/6.
If two lines are parallel, their slopes will be the same. If two lines are perpendicular, their slopes will be negative reciprocals of each other.
In this case, the slope of l1 is 6/5 and the slope of l2 is -5/6. These slopes are not the same, so the lines are not parallel.
To determine if they are perpendicular, we need to find the negative reciprocal of one of the slopes. The negative reciprocal of 6/5 is -5/6, which is the same as the slope of l2. Since the slopes are negative reciprocals, the lines l1 and l2 are perpendicular.
Therefore, the equations represent perpendicular lines.
To determine if the equations represent parallel lines, perpendicular lines, or neither, we need to compare the slopes of the two lines.
The given equations are:
l1: y = (6/5)x - (2/3)
l2: y = (-5/6)x - 1
The slopes of these equations are the coefficients of x in each equation. So, the slope of l1 is 6/5, and the slope of l2 is -5/6.
Two lines are parallel if and only if their slopes are equal. In this case, the slopes of l1 and l2 are not equal (6/5 ≠ -5/6), so the lines are not parallel.
Two lines are perpendicular if and only if the product of their slopes is -1. In this case, the product of the slopes of l1 and l2 is not -1 ((6/5)(-5/6) = -1), so the lines are not perpendicular either.
Since the slopes are neither equal nor the negative reciprocal of each other, we can conclude that the given equations represent neither parallel lines nor perpendicular lines.
To determine if the equations represent parallel lines, perpendicular lines, or neither, we can compare their slopes. The general form of a linear equation, y = mx + b, shows that "m" represents the slope of the line.
For line 1, the equation is y = (6/5)x - 2/3. Comparing this equation to the general form, we can see that the slope, or "m1", is 6/5.
For line 2, the equation is y = (-5/6)x - 1. Comparing this equation to the general form, we can see that the slope, or "m2", is -5/6.
Since the slopes of the lines, m1 and m2, are not the same, they are not parallel lines.
To determine if the lines are perpendicular, we can check if the product of their slopes is -1. If the product is -1, it means they are perpendicular.
Taking the product of the slopes: (6/5) * (-5/6) = -30/30 = -1.
Since the product of the slopes is -1, the lines are perpendicular.
In summary, the equations represent perpendicular lines.