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

Which set of ordered pairs (x,y) (x, y) could represent a linear function?\newlineA={(−1,0),(2,3),(5,6),(9,9)}B={(−2,9),(−1,6),(1,3),(3,0)}C={(0,5),(3,2),(6,−1),(9,−4)}D={(3,−8),(5,−4),(7,−1),(9,2)} \begin{array}{l} \mathbf{A}=\{(-1,0),(2,3),(5,6),(9,9)\} \\ \mathbf{B}=\{(-2,9),(-1,6),(1,3),(3,0)\} \\ \mathbf{C}=\{(0,5),(3,2),(6,-1),(9,-4)\} \\ \mathbf{D}=\{(3,-8),(5,-4),(7,-1),(9,2)\} \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={(−1,0),(2,3),(5,6),(9,9)}B={(−2,9),(−1,6),(1,3),(3,0)}C={(0,5),(3,2),(6,−1),(9,−4)}D={(3,−8),(5,−4),(7,−1),(9,2)} \begin{array}{l} \mathbf{A}=\{(-1,0),(2,3),(5,6),(9,9)\} \\ \mathbf{B}=\{(-2,9),(-1,6),(1,3),(3,0)\} \\ \mathbf{C}=\{(0,5),(3,2),(6,-1),(9,-4)\} \\ \mathbf{D}=\{(3,-8),(5,-4),(7,-1),(9,2)\} \end{array} \newlineA\newlineB\newlineC\newlineD
  1. Check Slope Set A: To determine if a set of ordered pairs represents a linear function, we need to check if the difference in yy-values divided by the difference in xx-values (the slope) is constant between every pair of points.
  2. Check Slope Set B: Let's start with set A: {(−1,0),(2,3),(5,6),(9,9)}\{(-1,0), (2,3), (5,6), (9,9)\}. Calculate the slope between the first two points: slope = y2−y1x2−x1=3−02−(−1)=33=1\frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 0}{2 - (-1)} = \frac{3}{3} = 1.
  3. Check Slope Set C: Now calculate the slope between the second and third points: slope = (6−3)/(5−2)=3/3=1(6 - 3) / (5 - 2) = 3 / 3 = 1.
  4. Check Slope Set D: Calculate the slope between the third and fourth points: slope = (9−6)/(9−5)=3/4(9 - 6) / (9 - 5) = 3 / 4. The slope is not the same as before, so set A does not represent a linear function.
  5. Check Slope Set D: Calculate the slope between the third and fourth points: slope=9−69−5=34\text{slope} = \frac{9 - 6}{9 - 5} = \frac{3}{4}. The slope is not the same as before, so set A does not represent a linear function.Now let's check set B: {(−2,9),(−1,6),(1,3),(3,0)}\{(-2,9), (-1,6), (1,3), (3,0)\}. Calculate the slope between the first two points: slope=6−9−1−(−2)=−31=−3\text{slope} = \frac{6 - 9}{-1 - (-2)} = \frac{-3}{1} = -3.
  6. Check Slope Set D: Calculate the slope between the third and fourth points: slope = (9−6)/(9−5)=3/4(9 - 6) / (9 - 5) = 3 / 4. The slope is not the same as before, so set A does not represent a linear function.Now let's check set B: {(−2,9),(−1,6),(1,3),(3,0)}\{(-2,9), (-1,6), (1,3), (3,0)\}. Calculate the slope between the first two points: slope = (6−9)/(−1−(−2))=(−3)/1=−3(6 - 9) / (-1 - (-2)) = (-3) / 1 = -3.Calculate the slope between the second and third points: slope = (3−6)/(1−(−1))=(−3)/2(3 - 6) / (1 - (-1)) = (-3) / 2. The slope is not the same as before, so set B does not represent a linear function.
  7. Check Slope Set D: Calculate the slope between the third and fourth points: slope=9−69−5=34\text{slope} = \frac{9 - 6}{9 - 5} = \frac{3}{4}. The slope is not the same as before, so set A does not represent a linear function. Now let's check set B: {(−2,9),(−1,6),(1,3),(3,0)}\{(-2,9), (-1,6), (1,3), (3,0)\}. Calculate the slope between the first two points: slope=6−9−1−(−2)=−31=−3\text{slope} = \frac{6 - 9}{-1 - (-2)} = \frac{-3}{1} = -3. Calculate the slope between the second and third points: slope=3−61−(−1)=−32\text{slope} = \frac{3 - 6}{1 - (-1)} = \frac{-3}{2}. The slope is not the same as before, so set B does not represent a linear function. Next, let's check set C: {(0,5),(3,2),(6,−1),(9,−4)}\{(0,5), (3,2), (6,-1), (9,-4)\}. 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.
  8. Check Slope Set D: Calculate the slope between the third and fourth points: slope=9−69−5=34\text{slope} = \frac{9 - 6}{9 - 5} = \frac{3}{4}. The slope is not the same as before, so set A does not represent a linear function. Now let's check set B: {(−2,9),(−1,6),(1,3),(3,0)}\{(-2,9), (-1,6), (1,3), (3,0)\}. Calculate the slope between the first two points: slope=6−9−1−(−2)=−31=−3\text{slope} = \frac{6 - 9}{-1 - (-2)} = \frac{-3}{1} = -3. Calculate the slope between the second and third points: slope=3−61−(−1)=−32\text{slope} = \frac{3 - 6}{1 - (-1)} = \frac{-3}{2}. The slope is not the same as before, so set B does not represent a linear function. Next, let's check set C: {(0,5),(3,2),(6,−1),(9,−4)}\{(0,5), (3,2), (6,-1), (9,-4)\}. 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.
  9. Check Slope Set D: Calculate the slope between the third and fourth points: slope=9−69−5=34\text{slope} = \frac{9 - 6}{9 - 5} = \frac{3}{4}. The slope is not the same as before, so set A does not represent a linear function.Now let's check set B: {(−2,9),(−1,6),(1,3),(3,0)}\{(-2,9), (-1,6), (1,3), (3,0)\}. Calculate the slope between the first two points: slope=6−9−1−(−2)=−31=−3\text{slope} = \frac{6 - 9}{-1 - (-2)} = \frac{-3}{1} = -3.Calculate the slope between the second and third points: slope=3−61−(−1)=−32\text{slope} = \frac{3 - 6}{1 - (-1)} = \frac{-3}{2}. The slope is not the same as before, so set B does not represent a linear function.Next, let's check set C: {(0,5),(3,2),(6,−1),(9,−4)}\{(0,5), (3,2), (6,-1), (9,-4)\}. 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=−4−(−1)9−6=−33=−1\text{slope} = \frac{-4 - (-1)}{9 - 6} = \frac{-3}{3} = -1. The slope is the same for all pairs of points, so set C does represent a linear function.
  10. Check Slope Set D: Calculate the slope between the third and fourth points: slope=9−69−5=34\text{slope} = \frac{9 - 6}{9 - 5} = \frac{3}{4}. The slope is not the same as before, so set A does not represent a linear function.Now let's check set B: {(−2,9),(−1,6),(1,3),(3,0)}\{(-2,9), (-1,6), (1,3), (3,0)\}. Calculate the slope between the first two points: slope=6−9−1−(−2)=−31=−3\text{slope} = \frac{6 - 9}{-1 - (-2)} = \frac{-3}{1} = -3.Calculate the slope between the second and third points: slope=3−61−(−1)=−32\text{slope} = \frac{3 - 6}{1 - (-1)} = \frac{-3}{2}. The slope is not the same as before, so set B does not represent a linear function.Next, let's check set C: {(0,5),(3,2),(6,−1),(9,−4)}\{(0,5), (3,2), (6,-1), (9,-4)\}. 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=−4−(−1)9−6=−33=−1\text{slope} = \frac{-4 - (-1)}{9 - 6} = \frac{-3}{3} = -1. The slope is the same for all pairs of points, so set C does represent a linear function.Finally, let's check set D: {(3,−8),(5,−4),(7,−1),(9,2)}\{(3,-8), (5,-4), (7,-1), (9,2)\}. Calculate the slope between the first two points: slope=−4−(−8)5−3=42=2\text{slope} = \frac{-4 - (-8)}{5 - 3} = \frac{4}{2} = 2.
  11. Check Slope Set D: Calculate the slope between the third and fourth points: slope=9−69−5=34\text{slope} = \frac{9 - 6}{9 - 5} = \frac{3}{4}. The slope is not the same as before, so set A does not represent a linear function.Now let's check set B: {(−2,9),(−1,6),(1,3),(3,0)}\{(-2,9), (-1,6), (1,3), (3,0)\}. Calculate the slope between the first two points: slope=6−9−1−(−2)=−31=−3\text{slope} = \frac{6 - 9}{-1 - (-2)} = \frac{-3}{1} = -3.Calculate the slope between the second and third points: slope=3−61−(−1)=−32\text{slope} = \frac{3 - 6}{1 - (-1)} = \frac{-3}{2}. The slope is not the same as before, so set B does not represent a linear function.Next, let's check set C: {(0,5),(3,2),(6,−1),(9,−4)}\{(0,5), (3,2), (6,-1), (9,-4)\}. 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=−4−(−1)9−6=−33=−1\text{slope} = \frac{-4 - (-1)}{9 - 6} = \frac{-3}{3} = -1. The slope is the same for all pairs of points, so set C does represent a linear function.Finally, let's check set D: {(3,−8),(5,−4),(7,−1),(9,2)}\{(3,-8), (5,-4), (7,-1), (9,2)\}. Calculate the slope between the first two points: slope=−4−(−8)5−3=42=2\text{slope} = \frac{-4 - (-8)}{5 - 3} = \frac{4}{2} = 2.Calculate the slope between the second and third points: {(−2,9),(−1,6),(1,3),(3,0)}\{(-2,9), (-1,6), (1,3), (3,0)\}00. The slope is not the same as before, so set D does not represent a linear function.

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