Determine if the equations represent parallel lines, perpendicular lines, or neither.
l1:y=6/5
l2:x=4
The equation l1: y = 6/5 represents a horizontal line because the y-value is constant at 6/5 while the x-value can be any number.
The equation l2: x = 4 represents a vertical line because the x-value is constant at 4 while the y-value can be any number.
Since a horizontal line and a vertical line are always perpendicular, we can conclude that 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 lines.
The slope of a line is represented by the coefficient of the x term in the equation. For l1:y=6/5, the equation is already in slope-intercept form, and we can see that the slope is 6/5.
For l2:x=4, we can rewrite it in slope-intercept form by considering that any number can be written as y/1. So, the equation becomes y/1 = 0 * x + 4, which simplifies to y = 4. Now we can see that the coefficient of the x term is 0, so the slope is 0.
Since the slope of l1 is 6/5 and the slope of l2 is 0, we can conclude that the lines are neither parallel nor perpendicular.
To determine whether two lines are parallel, perpendicular, or neither, we need to analyze their slopes.
For l1: y = 6/5
The equation y = 6/5 is in the form y = mx + b, where m represents the slope. In this case, "m" is equal to 6/5. Since this equation only has the variable y and no variable x, it implies that the line is horizontal and has a slope of 0.
For l2: x = 4
The equation x = 4 is in the form x = c, where c is a constant value. Since this equation only has the variable x and no variable y, it implies that the line is vertical and has an undefined slope.
Now, to determine the relationship between the two lines:
If two lines are parallel, they have the same slope.
If two lines are perpendicular, their slopes are negative reciprocals of each other.
If two lines have different slopes and are not negative reciprocals of each other, then they are neither parallel nor perpendicular.
In this case, the slope of l1 is 0, and the slope of l2 is undefined. Since these slopes are neither the same nor negative reciprocals of each other, l1 and l2 are neither parallel nor perpendicular.