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Which set of ordered pairs (x,y) could represent a linear function? {:[A={(-4","0)","(-1","3)","(2","6)","(5","8)}],[B={(0","5)","(3","2)","(6","-1)","(9","-5)}],[C={(-1","7)","(0","5)","(2","1)","(3","-1)}],[D={(-9","-7)","(-3","-4)","(2","-1)","(8","2)}]:} A B C D

Which set of ordered pairs (x,y) (x, y) could represent a linear function?\newlineA={(−4,0),(−1,3),(2,6),(5,8)}B={(0,5),(3,2),(6,−1),(9,−5)}C={(−1,7),(0,5),(2,1),(3,−1)}D={(−9,−7),(−3,−4),(2,−1),(8,2)} \begin{array}{l} \mathbf{A}=\{(-4,0),(-1,3),(2,6),(5,8)\} \\ \mathbf{B}=\{(0,5),(3,2),(6,-1),(9,-5)\} \\ \mathbf{C}=\{(-1,7),(0,5),(2,1),(3,-1)\} \\ \mathbf{D}=\{(-9,-7),(-3,-4),(2,-1),(8,2)\} \end{array} \newlineA\newlineB\newlineC\newlineD

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Q. Which set of ordered pairs (x,y) (x, y) could represent a linear function?\newlineA={(−4,0),(−1,3),(2,6),(5,8)}B={(0,5),(3,2),(6,−1),(9,−5)}C={(−1,7),(0,5),(2,1),(3,−1)}D={(−9,−7),(−3,−4),(2,−1),(8,2)} \begin{array}{l} \mathbf{A}=\{(-4,0),(-1,3),(2,6),(5,8)\} \\ \mathbf{B}=\{(0,5),(3,2),(6,-1),(9,-5)\} \\ \mathbf{C}=\{(-1,7),(0,5),(2,1),(3,-1)\} \\ \mathbf{D}=\{(-9,-7),(-3,-4),(2,-1),(8,2)\} \end{array} \newlineA\newlineB\newlineC\newlineD
  1. Calculate Slope Set A: To determine if a set of ordered pairs represents a linear function, we need to check if the rate of change (slope) between each pair of points is constant. The slope between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is calculated by (y2−y1)/(x2−x1)(y_2 - y_1) / (x_2 - x_1).
  2. Calculate Slope Set B: Let's start with set A: (−4,0),(−1,3),(2,6),(5,8){(-4, 0), (-1, 3), (2, 6), (5, 8)}. Calculate the slope between the first two points: slope=3−0−1−(−4)=33=1\text{slope} = \frac{3 - 0}{-1 - (-4)} = \frac{3}{3} = 1.
  3. Calculate Slope Set C: Now calculate the slope between the second and third points: slope=6−32−(−1)=33=1\text{slope} = \frac{6 - 3}{2 - (-1)} = \frac{3}{3} = 1.
  4. Calculate Slope Set D: Calculate the slope between the third and fourth points: slope=8−65−2=23\text{slope} = \frac{8 - 6}{5 - 2} = \frac{2}{3}.
  5. Calculate Slope Set D: Calculate the slope between the third and fourth points: slope=8−65−2=23slope = \frac{8 - 6}{5 - 2} = \frac{2}{3}.Since the slope between the third and fourth points is not equal to the slope between the first two pairs of points, set A does not represent a linear function.
  6. Calculate Slope Set D: Calculate the slope between the third and fourth points: slope=8−65−2=23\text{slope} = \frac{8 - 6}{5 - 2} = \frac{2}{3}.Since the slope between the third and fourth points is not equal to the slope between the first two pairs of points, set A does not represent a linear function.Now let's check set B: {(0,5),(3,2),(6,−1),(9,−5)}\{(0, 5), (3, 2), (6, -1), (9, -5)\}. Calculate the slope between the first two points: slope=2−53−0=−33=−1\text{slope} = \frac{2 - 5}{3 - 0} = \frac{-3}{3} = -1.
  7. Calculate Slope Set D: Calculate the slope between the third and fourth points: slope=8−65−2=23\text{slope} = \frac{8 - 6}{5 - 2} = \frac{2}{3}.Since the slope between the third and fourth points is not equal to the slope between the first two pairs of points, set A does not represent a linear function.Now let's check set B: {(0,5),(3,2),(6,−1),(9,−5)}\{(0, 5), (3, 2), (6, -1), (9, -5)\}. Calculate the slope between the first two points: slope=2−53−0=−33=−1\text{slope} = \frac{2 - 5}{3 - 0} = \frac{-3}{3} = -1.Calculate the slope between the second and third points: slope=−1−26−3=−33=−1\text{slope} = \frac{-1 - 2}{6 - 3} = \frac{-3}{3} = -1.
  8. Calculate Slope Set D: Calculate the slope between the third and fourth points: slope=8−65−2=23slope = \frac{8 - 6}{5 - 2} = \frac{2}{3}.Since the slope between the third and fourth points is not equal to the slope between the first two pairs of points, set A does not represent a linear function.Now let's check set B: {(0,5),(3,2),(6,−1),(9,−5)}\{(0, 5), (3, 2), (6, -1), (9, -5)\}. Calculate the slope between the first two points: slope=2−53−0=−33=−1slope = \frac{2 - 5}{3 - 0} = \frac{-3}{3} = -1.Calculate the slope between the second and third points: slope=−1−26−3=−33=−1slope = \frac{-1 - 2}{6 - 3} = \frac{-3}{3} = -1.Calculate the slope between the third and fourth points: slope=−5−(−1)9−6=−43slope = \frac{-5 - (-1)}{9 - 6} = \frac{-4}{3}.
  9. Calculate Slope Set D: Calculate the slope between the third and fourth points: slope=8−65−2=23slope = \frac{8 - 6}{5 - 2} = \frac{2}{3}.Since the slope between the third and fourth points is not equal to the slope between the first two pairs of points, set A does not represent a linear function.Now let's check set B: {(0,5),(3,2),(6,−1),(9,−5)}\{(0, 5), (3, 2), (6, -1), (9, -5)\}. Calculate the slope between the first two points: slope=2−53−0=−33=−1slope = \frac{2 - 5}{3 - 0} = \frac{-3}{3} = -1.Calculate the slope between the second and third points: slope=−1−26−3=−33=−1slope = \frac{-1 - 2}{6 - 3} = \frac{-3}{3} = -1.Calculate the slope between the third and fourth points: slope=−5−(−1)9−6=−43slope = \frac{-5 - (-1)}{9 - 6} = \frac{-4}{3}.Since the slope between the third and fourth points is not equal to the slope between the first two pairs of points, set B does not represent a linear function.
  10. Calculate Slope Set D: Calculate the slope between the third and fourth points: slope=8−65−2=23slope = \frac{8 - 6}{5 - 2} = \frac{2}{3}. Since the slope between the third and fourth points is not equal to the slope between the first two pairs of points, set A does not represent a linear function. Now let's check set B: {(0,5),(3,2),(6,−1),(9,−5)}\{(0, 5), (3, 2), (6, -1), (9, -5)\}. Calculate the slope between the first two points: slope=2−53−0=−33=−1slope = \frac{2 - 5}{3 - 0} = \frac{-3}{3} = -1. Calculate the slope between the second and third points: slope=−1−26−3=−33=−1slope = \frac{-1 - 2}{6 - 3} = \frac{-3}{3} = -1. Calculate the slope between the third and fourth points: slope=−5−(−1)9−6=−43slope = \frac{-5 - (-1)}{9 - 6} = \frac{-4}{3}. Since the slope between the third and fourth points is not equal to the slope between the first two pairs of points, set B does not represent a linear function. Now let's check set C: {(−1,7),(0,5),(2,1),(3,−1)}\{(-1, 7), (0, 5), (2, 1), (3, -1)\}. Calculate the slope between the first two points: slope=5−70−(−1)=−21=−2slope = \frac{5 - 7}{0 - (-1)} = \frac{-2}{1} = -2.
  11. Calculate Slope Set D: Calculate the slope between the third and fourth points: slope=8−65−2=23\text{slope} = \frac{8 - 6}{5 - 2} = \frac{2}{3}. Since the slope between the third and fourth points is not equal to the slope between the first two pairs of points, set A does not represent a linear function. Now let's check set B: {(0,5),(3,2),(6,−1),(9,−5)}\{(0, 5), (3, 2), (6, -1), (9, -5)\}. Calculate the slope between the first two points: slope=2−53−0=−33=−1\text{slope} = \frac{2 - 5}{3 - 0} = \frac{-3}{3} = -1. Calculate the slope between the second and third points: slope=−1−26−3=−33=−1\text{slope} = \frac{-1 - 2}{6 - 3} = \frac{-3}{3} = -1. Calculate the slope between the third and fourth points: slope=−5−(−1)9−6=−43\text{slope} = \frac{-5 - (-1)}{9 - 6} = \frac{-4}{3}. Since the slope between the third and fourth points is not equal to the slope between the first two pairs of points, set B does not represent a linear function. Now let's check set C: {(−1,7),(0,5),(2,1),(3,−1)}\{(-1, 7), (0, 5), (2, 1), (3, -1)\}. Calculate the slope between the first two points: slope=5−70−(−1)=−21=−2\text{slope} = \frac{5 - 7}{0 - (-1)} = \frac{-2}{1} = -2. Calculate the slope between the second and third points: slope=1−52−0=−42=−2\text{slope} = \frac{1 - 5}{2 - 0} = \frac{-4}{2} = -2.
  12. Calculate Slope Set D: Calculate the slope between the third and fourth points: slope = (8−6)/(5−2)=2/3(8 - 6) / (5 - 2) = 2 / 3. Since the slope between the third and fourth points is not equal to the slope between the first two pairs of points, set A does not represent a linear function. Now let's check set B: {(0,5),(3,2),(6,−1),(9,−5)}\{(0, 5), (3, 2), (6, -1), (9, -5)\}. Calculate the slope between the first two points: slope = (2−5)/(3−0)=−3/3=−1(2 - 5) / (3 - 0) = -3 / 3 = -1. Calculate the slope between the second and third points: slope = (−1−2)/(6−3)=−3/3=−1(-1 - 2) / (6 - 3) = -3 / 3 = -1. Calculate the slope between the third and fourth points: slope = (−5−(−1))/(9−6)=−4/3(-5 - (-1)) / (9 - 6) = -4 / 3. Since the slope between the third and fourth points is not equal to the slope between the first two pairs of points, set B does not represent a linear function. Now let's check set C: {(−1,7),(0,5),(2,1),(3,−1)}\{(-1, 7), (0, 5), (2, 1), (3, -1)\}. Calculate the slope between the first two points: slope = (5−7)/(0−(−1))=−2/1=−2(5 - 7) / (0 - (-1)) = -2 / 1 = -2. Calculate the slope between the second and third points: slope = (1−5)/(2−0)=−4/2=−2(1 - 5) / (2 - 0) = -4 / 2 = -2. Calculate the slope between the third and fourth points: slope = (−1−1)/(3−2)=−2/1=−2(-1 - 1) / (3 - 2) = -2 / 1 = -2.
  13. Calculate Slope Set D: Calculate the slope between the third and fourth points: slope=8−65−2=23slope = \frac{8 - 6}{5 - 2} = \frac{2}{3}.Since the slope between the third and fourth points is not equal to the slope between the first two pairs of points, set A does not represent a linear function.Now let's check set B: {(0,5),(3,2),(6,−1),(9,−5)}\{(0, 5), (3, 2), (6, -1), (9, -5)\}. Calculate the slope between the first two points: slope=2−53−0=−33=−1slope = \frac{2 - 5}{3 - 0} = \frac{-3}{3} = -1.Calculate the slope between the second and third points: slope=−1−26−3=−33=−1slope = \frac{-1 - 2}{6 - 3} = \frac{-3}{3} = -1.Calculate the slope between the third and fourth points: slope=−5−(−1)9−6=−43slope = \frac{-5 - (-1)}{9 - 6} = \frac{-4}{3}.Since the slope between the third and fourth points is not equal to the slope between the first two pairs of points, set B does not represent a linear function.Now let's check set C: {(−1,7),(0,5),(2,1),(3,−1)}\{(-1, 7), (0, 5), (2, 1), (3, -1)\}. Calculate the slope between the first two points: slope=5−70−(−1)=−21=−2slope = \frac{5 - 7}{0 - (-1)} = \frac{-2}{1} = -2.Calculate the slope between the second and third points: slope=1−52−0=−42=−2slope = \frac{1 - 5}{2 - 0} = \frac{-4}{2} = -2.Calculate the slope between the third and fourth points: slope=−1−13−2=−21=−2slope = \frac{-1 - 1}{3 - 2} = \frac{-2}{1} = -2.Since the slope is constant between all pairs of points, set C represents a linear function.
  14. Calculate Slope Set D: Calculate the slope between the third and fourth points: slope=8−65−2=23\text{slope} = \frac{8 - 6}{5 - 2} = \frac{2}{3}. Since the slope between the third and fourth points is not equal to the slope between the first two pairs of points, set A does not represent a linear function. Now let's check set B: {(0,5),(3,2),(6,−1),(9,−5)}\{(0, 5), (3, 2), (6, -1), (9, -5)\}. Calculate the slope between the first two points: slope=2−53−0=−33=−1\text{slope} = \frac{2 - 5}{3 - 0} = \frac{-3}{3} = -1. Calculate the slope between the second and third points: slope=−1−26−3=−33=−1\text{slope} = \frac{-1 - 2}{6 - 3} = \frac{-3}{3} = -1. Calculate the slope between the third and fourth points: slope=−5−(−1)9−6=−43\text{slope} = \frac{-5 - (-1)}{9 - 6} = \frac{-4}{3}. Since the slope between the third and fourth points is not equal to the slope between the first two pairs of points, set B does not represent a linear function. Now let's check set C: {(−1,7),(0,5),(2,1),(3,−1)}\{(-1, 7), (0, 5), (2, 1), (3, -1)\}. Calculate the slope between the first two points: slope=5−70−(−1)=−21=−2\text{slope} = \frac{5 - 7}{0 - (-1)} = \frac{-2}{1} = -2. Calculate the slope between the second and third points: slope=1−52−0=−42=−2\text{slope} = \frac{1 - 5}{2 - 0} = \frac{-4}{2} = -2. Calculate the slope between the third and fourth points: slope=−1−13−2=−21=−2\text{slope} = \frac{-1 - 1}{3 - 2} = \frac{-2}{1} = -2. Since the slope is constant between all pairs of points, set C represents a linear function. Finally, let's check set D: {(−9,−7),(−3,−4),(2,−1),(8,2)}\{(-9, -7), (-3, -4), (2, -1), (8, 2)\}. Calculate the slope between the first two points: {(0,5),(3,2),(6,−1),(9,−5)}\{(0, 5), (3, 2), (6, -1), (9, -5)\}00.
  15. Calculate Slope Set D: Calculate the slope between the third and fourth points: slope=8−65−2=23slope = \frac{8 - 6}{5 - 2} = \frac{2}{3}.Since the slope between the third and fourth points is not equal to the slope between the first two pairs of points, set A does not represent a linear function.Now let's check set B: {(0,5),(3,2),(6,−1),(9,−5)}\{(0, 5), (3, 2), (6, -1), (9, -5)\}. Calculate the slope between the first two points: slope=2−53−0=−33=−1slope = \frac{2 - 5}{3 - 0} = \frac{-3}{3} = -1.Calculate the slope between the second and third points: slope=−1−26−3=−33=−1slope = \frac{-1 - 2}{6 - 3} = \frac{-3}{3} = -1.Calculate the slope between the third and fourth points: slope=−5−(−1)9−6=−43slope = \frac{-5 - (-1)}{9 - 6} = \frac{-4}{3}.Since the slope between the third and fourth points is not equal to the slope between the first two pairs of points, set B does not represent a linear function.Now let's check set C: {(−1,7),(0,5),(2,1),(3,−1)}\{(-1, 7), (0, 5), (2, 1), (3, -1)\}. Calculate the slope between the first two points: slope=5−70−(−1)=−21=−2slope = \frac{5 - 7}{0 - (-1)} = \frac{-2}{1} = -2.Calculate the slope between the second and third points: slope=1−52−0=−42=−2slope = \frac{1 - 5}{2 - 0} = \frac{-4}{2} = -2.Calculate the slope between the third and fourth points: slope=−1−13−2=−21=−2slope = \frac{-1 - 1}{3 - 2} = \frac{-2}{1} = -2.Since the slope is constant between all pairs of points, set C represents a linear function.Finally, let's check set D: {(−9,−7),(−3,−4),(2,−1),(8,2)}\{(-9, -7), (-3, -4), (2, -1), (8, 2)\}. Calculate the slope between the first two points: {(0,5),(3,2),(6,−1),(9,−5)}\{(0, 5), (3, 2), (6, -1), (9, -5)\}00.Calculate the slope between the second and third points: {(0,5),(3,2),(6,−1),(9,−5)}\{(0, 5), (3, 2), (6, -1), (9, -5)\}11.
  16. Calculate Slope Set D: Calculate the slope between the third and fourth points: slope=8−65−2=23slope = \frac{8 - 6}{5 - 2} = \frac{2}{3}.Since the slope between the third and fourth points is not equal to the slope between the first two pairs of points, set A does not represent a linear function.Now let's check set B: {(0,5),(3,2),(6,−1),(9,−5)}\{(0, 5), (3, 2), (6, -1), (9, -5)\}. Calculate the slope between the first two points: slope=2−53−0=−33=−1slope = \frac{2 - 5}{3 - 0} = \frac{-3}{3} = -1.Calculate the slope between the second and third points: slope=−1−26−3=−33=−1slope = \frac{-1 - 2}{6 - 3} = \frac{-3}{3} = -1.Calculate the slope between the third and fourth points: slope=−5−(−1)9−6=−43slope = \frac{-5 - (-1)}{9 - 6} = \frac{-4}{3}.Since the slope between the third and fourth points is not equal to the slope between the first two pairs of points, set B does not represent a linear function.Now let's check set C: {(−1,7),(0,5),(2,1),(3,−1)}\{(-1, 7), (0, 5), (2, 1), (3, -1)\}. Calculate the slope between the first two points: slope=5−70−(−1)=−21=−2slope = \frac{5 - 7}{0 - (-1)} = \frac{-2}{1} = -2.Calculate the slope between the second and third points: slope=1−52−0=−42=−2slope = \frac{1 - 5}{2 - 0} = \frac{-4}{2} = -2.Calculate the slope between the third and fourth points: slope=−1−13−2=−21=−2slope = \frac{-1 - 1}{3 - 2} = \frac{-2}{1} = -2.Since the slope is constant between all pairs of points, set C represents a linear function.Finally, let's check set D: {(−9,−7),(−3,−4),(2,−1),(8,2)}\{(-9, -7), (-3, -4), (2, -1), (8, 2)\}. Calculate the slope between the first two points: {(0,5),(3,2),(6,−1),(9,−5)}\{(0, 5), (3, 2), (6, -1), (9, -5)\}00.Calculate the slope between the second and third points: {(0,5),(3,2),(6,−1),(9,−5)}\{(0, 5), (3, 2), (6, -1), (9, -5)\}11.Since the slope between the second and third points is not equal to the slope between the first two points, set D does not represent a linear function.

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