Which set of ordered pairs left bracket, x, comma, y, right bracket(x,y) could represent a linear function?
A, equals, left curly bracket, left bracket, 2, comma, 7, right bracket, comma, left bracket, 3, comma, 5, right bracket, comma, left bracket, 4, comma, 2, right bracket, comma, left bracket, 6, comma, minus, 4, right bracket, right curly bracket
A=
{(2,7),(3,5),(4,2),(6,−4)}
B, equals, left curly bracket, left bracket, 1, comma, minus, 6, right bracket, comma, left bracket, 2, comma, minus, 4, right bracket, comma, left bracket, 3, comma, minus, 2, right bracket, comma, left bracket, 4, comma, 0, right bracket, right curly bracket
B=
{(1,−6),(2,−4),(3,−2),(4,0)}
C, equals, left curly bracket, left bracket, minus, 3, comma, 2, right bracket, comma, left bracket, 0, comma, 1, right bracket, comma, left bracket, 2, comma, 0, right bracket, comma, left bracket, 4, comma, minus, 1, right bracket, right curly bracket
C=
{(−3,2),(0,1),(2,0),(4,−1)}
D, equals, left curly bracket, left bracket, minus, 4, comma, minus, 3, right bracket, comma, left bracket, minus, 1, comma, 0, right bracket, comma, left bracket, 2, comma, 3, right bracket, comma, left bracket, 6, comma, 6, right bracket, right curly bracket
D=
{(−4,−3),(−1,0),(2,3),(6,6)}
B= {(1,−6),(2,−4),(3,−2),(4,0)}
The set of ordered pairs that could represent a linear function is B.
B= {(1,−6),(2,−4),(3,−2),(4,0)}
In this set, the y-values change by a consistent amount as the x-values increase. This indicates a proportional relationship and suggests a linear function.
To determine which set of ordered pairs represents a linear function, we need to check if there is a constant rate of change between the x and y values.
A linear function has a constant rate of change, which means that for every change of 1 in the x-coordinate, there is a consistent change in the y-coordinate.
Let's calculate the rate of change for each set of ordered pairs:
A:
(2,7) to (3,5): For x changing from 2 to 3, y changes from 7 to 5. The rate of change is (5-7)/(3-2) = -2.
(3,5) to (4,2): For x changing from 3 to 4, y changes from 5 to 2. The rate of change is (2-5)/(4-3) = -3.
(4,2) to (6,-4): For x changing from 4 to 6, y changes from 2 to -4. The rate of change is (-4-2)/(6-4) = -3.
Since the rate of change is not consistent, set A does not represent a linear function.
Let's calculate the rate of change for set B:
B:
(1,-6) to (2,-4): For x changing from 1 to 2, y changes from -6 to -4. The rate of change is (-4-(-6))/(2-1) = 2.
(2,-4) to (3,-2): For x changing from 2 to 3, y changes from -4 to -2. The rate of change is (-2-(-4))/(3-2) = 2.
(3,-2) to (4,0): For x changing from 3 to 4, y changes from -2 to 0. The rate of change is (0-(-2))/(4-3) = 2.
The rate of change is consistent in set B, so it represents a linear function.
Let's calculate the rate of change for set C:
C:
(-3,2) to (0,1): For x changing from -3 to 0, y changes from 2 to 1. The rate of change is (1-2)/(0-(-3)) = -1/3.
(0,1) to (2,0): For x changing from 0 to 2, y changes from 1 to 0. The rate of change is (0-1)/(2-0) = -1/2.
(2,0) to (4,-1): For x changing from 2 to 4, y changes from 0 to -1. The rate of change is (-1-0)/(4-2) = -1/2.
The rate of change is not consistent in set C, so it does not represent a linear function.
Let's calculate the rate of change for set D:
D:
(-4,-3) to (-1,0): For x changing from -4 to -1, y changes from -3 to 0. The rate of change is (0-(-3))/(-1-(-4)) = 1.
(-1,0) to (2,3): For x changing from -1 to 2, y changes from 0 to 3. The rate of change is (3-0)/(2-(-1)) = 1.
(2,3) to (6,6): For x changing from 2 to 6, y changes from 3 to 6. The rate of change is (6-3)/(6-2) = 1.
The rate of change is consistent in set D, so it represents a linear function.
Therefore, the set of ordered pairs that represents a linear function is B: {(1,-6),(2,-4),(3,-2),(4,0)}.