Determine if the equations represent parallel lines, perpendicular lines, or neither.
l1: 7y=9
l2: y=4
To determine if two lines are parallel, perpendicular, or neither, we need to compare their slopes.
The given equations are:
l1: 7y = 9
l2: y = 4
To compare their slopes, we need to rewrite the equations in slope-intercept form (y = mx + b), where "m" represents the slope.
Rewriting l1 equation in slope-intercept form:
7y = 9
y = 9/7
The slope of l1 is 0.
Rewriting l2 equation in slope-intercept form:
y = 4
The slope of l2 is also 0.
Since both slopes are 0, the lines are parallel.
Therefore, the equations represent parallel lines.
To determine if two lines are parallel, perpendicular, or neither, we need to compare their slopes. The slope of a linear equation can be found by rearranging the equation into slope-intercept form (y = mx + b), where "m" represents the slope.
For the first equation, l1: 7y = 9, we can rearrange it to find its slope:
7y = 9
y = 9/7 (dividing both sides by 7)
The slope of l1 is 9/7.
For the second equation, l2: y = 4, it is already in slope-intercept form. By comparison, we can see its slope is 0.
The slope of l2 is 0.
Now, we can compare the slopes:
- If the slopes are equal, the lines are parallel.
- If the slopes are negative reciprocals of each other (e.g., 2 and -1/2), the lines are perpendicular.
- If the slopes are neither equal nor negative reciprocals, the lines are neither parallel nor perpendicular.
In this case, the slope of l1 is 9/7, and the slope of l2 is 0. Since the slopes are neither equal nor negative reciprocals, l1 and l2 are neither parallel nor perpendicular.
l1: 7y = 9 can be rearranged to y = 9/7
l2: y = 4
Since the slopes of both lines are different (l1 has a slope of 0 and l2 has a slope of 1), the lines are not parallel.
Since the product of the slopes is not -1, the lines are not perpendicular.
Therefore, the lines are neither parallel nor perpendicular.