Determine whether the lines are parallel, perpendicular, or neither.
# 1) y = 5( 4x + 9) and y = - 1/20x - 4
A) Parallel
B) Perpendicular
C) Neither
#2) y = 9x + 9 and y = -9x + 9
A) Parallel
B) Perpendicular
C) Neither
1. 5(4X + 9) and Y = -1/20X -4.
Y = 20X + 45
The slopes are negative reriprocals.
Therefore, the are perpendicular.
2. Y = 9X + 9 and y = -9X + 9.
Ans: neither.
To determine whether two lines are parallel, perpendicular, or neither, we need to compare their slopes.
For the first set of equations:
1) y = 5(4x + 9)
y = 20x + 45 (Distribute 5 to 4x and 9)
2) y = -1/20x - 4
The first equation is in slope-intercept form (y = mx + b), where the slope (m) is the coefficient of x. This means the slope of the first line is 20.
The second equation is also in slope-intercept form, and its slope is -1/20.
Now, let's compare the slopes:
For the first set of equations:
1) m1 = 20
2) m2 = -1/20
Since the slopes are not equal, the lines are not parallel.
To determine if they are perpendicular, we know that perpendicular lines have slopes that are negative reciprocals of each other. In other words, multiplying the slopes together should give us a product of -1.
Let's calculate:
m1 * m2 = 20 * (-1/20) = -1
The product is indeed -1. Therefore, the lines are perpendicular.
So the answer to the first set of equations is:
A) Parallel
For the second set of equations:
1) y = 9x + 9
2) y = -9x + 9
Comparing the slopes:
1) m1 = 9
2) m2 = -9
Since the slopes are not equal, the lines are not parallel.
To determine if they are perpendicular, we need to calculate the product of the slopes:
m1 * m2 = 9 * (-9) = -81
The product is not -1. Therefore, the lines are not perpendicular.
So the answer to the second set of equations is:
C) Neither