Question (C) Watch Video Show Examples Which set of ordered pairs $(x, y)$ could represent a linear function? \[ \begin{array}{l} \mathbf{A}=\{(-6,5),(-3,2),(0,-1),(3,-4)\} \\ \mathbf{B}=\{(-3,5),(-1,4),(1,3),(4,1)\} \\ \mathbf{C}=\{(2,-3),(4,-1),(7,1),(9,3)\} \\ \mathbf{D}=\{(-6,9),(-4,3),(-1,-3),(2,-9)\} \end{array} \] Answer A B C D
Solution
Step 1 ：Calculate the slope for each set of ordered pairs in option A using the formula \((y2 - y1) / (x2 - x1)\).
Step 2 ：The slope between the first two points in A is \((-3 / 3) = -1\).
Step 3 ：The slope between the second and third points in A is \((-3 / 3) = -1\).
Step 4 ：The slope between the third and fourth points in A is \((-3 / 3) = -1\).
Step 5 ：Since all the slopes in A are the same, A could represent a linear function.
Step 6 ：Calculate the slope for each set of ordered pairs in option B using the formula \((y2 - y1) / (x2 - x1)\).
Step 7 ：The slope between the first two points in B is \((-1 / 2) = -0.5\).
Step 8 ：The slope between the second and third points in B is \((-1 / 2) = -0.5\).
Step 9 ：The slope between the third and fourth points in B is \((-2 / 3) = -0.67\).
Step 10 ：Since all the slopes in B are not the same, B could not represent a linear function.
Step 11 ：Calculate the slope for each set of ordered pairs in option C using the formula \((y2 - y1) / (x2 - x1)\).
Step 12 ：The slope between the first two points in C is \((2 / 2) = 1\).
Step 13 ：The slope between the second and third points in C is \((2 / 3) = 0.67\).
Step 14 ：The slope between the third and fourth points in C is \((2 / 2) = 1\).
Step 15 ：Since all the slopes in C are not the same, C could not represent a linear function.
Step 16 ：Calculate the slope for each set of ordered pairs in option D using the formula \((y2 - y1) / (x2 - x1)\).
Step 17 ：The slope between the first two points in D is \((-6 / 2) = -3\).
Step 18 ：The slope between the second and third points in D is \((-6 / 3) = -2\).
Step 19 ：The slope between the third and fourth points in D is \((-6 / 3) = -2\).
Step 20 ：Since all the slopes in D are not the same, D could not represent a linear function.
Step 21 ：Therefore, the answer is \(\boxed{A}\).
