Which of the following pairs of equations are perpendicular?
3x + y = 9 and y = 3x – 3
8x – 7y = 9 and 2x + 6y = 2
3x – y = 7 and y = 3x + 9
x + 9 = y and y + x = 3
The pairs of equations that are perpendicular are:
3x + y = 9 and y = 3x - 3
Which function has the greater rate of change?
A) y = 2x + 4
B)
x y
1 2
2 4
3 6
4 8
A
B
Both A and B
None of the choices
To determine the rate of change of each function, we can look at the change in y divided by the change in x.
For function A, the rate of change is 2, because for every increase of 1 in x, there is an increase of 2 in y.
For function B, the rate of change is also 2, because for every increase of 1 in x, there is also an increase of 2 in y.
Therefore, both function A and function B have the same rate of change, which is 2. The answer is "Both A and B".
To determine if two equations are perpendicular, we can compare their slopes. If the product of the slopes is -1, then the lines are perpendicular.
Let's analyze each pair of equations:
1. 3x + y = 9 and y = 3x - 3:
The slope of the first equation is -3/1 = -3.
The slope of the second equation is 3.
The product of the slopes is -3 * 3 = -9, so these lines are not perpendicular.
2. 8x - 7y = 9 and 2x + 6y = 2:
The slope of the first equation is 8/7.
The slope of the second equation is -2/6 = -1/3.
The product of the slopes is (8/7) * (-1/3) = -8/21, so these lines are not perpendicular.
3. 3x - y = 7 and y = 3x + 9:
The slope of the first equation is 3/1 = 3.
The slope of the second equation is 3.
The product of the slopes is 3 * 3 = 9, so these lines are not perpendicular.
4. x + 9 = y and y + x = 3:
Rewrite the second equation in slope-intercept form: y = -x + 3.
The slope of the first equation is 1.
The slope of the second equation is -1.
The product of the slopes is 1 * (-1) = -1, so these lines are perpendicular.
Therefore, the pair of equations x + 9 = y and y + x = 3 is perpendicular.