Are the two lines parallel, perpendicular, or neither?
2x + 2y = 20; 3y = -3x + 50
The two lines are neither parallel nor perpendicular.
To determine if the two lines are parallel, perpendicular, or neither, we need to compare their slopes.
First, let's convert both equations to the slope-intercept form (y = mx + b), where m represents the slope.
For the first equation: 2x + 2y = 20
Rearranging, we get: 2y = -2x + 20
Dividing both sides by 2, we have: y = -x + 10
So, the slope of the first line is -1.
For the second equation: 3y = -3x + 50
Dividing both sides by 3, we get: y = -x/3 + 50/3
So, the slope of the second line is -1/3.
Since the slopes of the two lines are not equal, they are neither parallel nor perpendicular.
To determine whether the two lines are parallel, perpendicular, or neither, we need to compare their slopes.
First, let's put both equations in slope-intercept form (y = mx + b) by isolating y:
2x + 2y = 20
2y = -2x + 20
y = -x + 10
3y = -3x + 50
y = (-3x + 50) / 3
y = -x + 50/3
Comparing the coefficients of x, we can see that the slope of the first line is -1, and the slope of the second line is also -1.
Since the slopes of the lines are the same, the lines are parallel.
In summary, the two lines are parallel.