Determine if the equations represent parallel lines, perpendicular lines, or neither.
l1: 5x=10
l2: 6=x
To determine if two lines are parallel, perpendicular, or neither, we can compare the slopes of the two lines.
For equation l1: 5x = 10, we can write this in slope-intercept form: y = mx + b. This is already in this form, with y = 0x + 2 or y = 2. So the slope of l1 is 0.
For equation l2: 6 = x, we can also write this in slope-intercept form: y = mx + b. This can be written as y = 1x + 6, so the slope of l2 is 1.
Since the slope of l1 is 0 and the slope of l2 is 1, these lines are neither parallel nor perpendicular.
To determine if the equations represent parallel lines, perpendicular lines, or neither, we need to examine their slopes.
For line 1 (l1):
To get the equation in the form of y = mx + b, we divide the equation by 5: x = 2. This represents a vertical line passing through the point (2, 0).
For line 2 (l2):
The equation x = 6 represents a vertical line passing through the point (6, y).
Since both lines are vertical, they are parallel to each other.
To determine if the equations represent parallel lines, perpendicular lines, or neither, we need to compare their slopes.
For the equation of a line in the form of y = mx + b, where m is the slope, the given equations would be rewritten as:
l1: 5x - 10 = 0 => y = 0x + 2 (since 5x - 10 = 0 can be simplified to x = 2)
l2: x - 6 = 0 => y = 0x - 6 (since x - 6 = 0 can be simplified to x = 6)
From these forms, we can observe that the slopes are 0 for both equations.
Now, let's analyze the cases:
1. If the slopes of two lines are equal, then the lines are parallel.
2. If the product of the slopes of two lines is -1, then the lines are perpendicular.
3. If neither of the above conditions is satisfied, then the lines are neither parallel nor perpendicular.
In this scenario, since both lines have a slope of 0 (0 * 0 = 0), the product of their slopes is not -1. Therefore, the lines l1: 5x - 10 = 0 and l2: x - 6 = 0 are neither parallel nor perpendicular.