Which of the following is an ordered pair of the relation y=−2/3x+6 ?(1 point)
Responses
There are no options given to choose from. Please provide the available options for the ordered pair.
(3,4)
left parenthesis 3 comma 4 right parenthesis
(0,−23)
left parenthesis 0 comma negative Start Fraction 2 over 3 End Fraction right parenthesis
(1,4)
left parenthesis 1 comma 4 right parenthesis
(3,8)
To determine whether an ordered pair is a solution to the given equation, substitute the values of x and y into the equation and see if it is true.
Using the equation y = -2/3x + 6:
For (3,4), substitute x = 3 and y = 4 into the equation:
4 = (-2/3)(3) + 6
4 = -2 + 6
4 = 4
Since the equation is true, (3,4) is an ordered pair of the relation.
For (0,-23), substitute x = 0 and y = -23 into the equation:
-23 = (-2/3)(0) + 6
-23 = 0 + 6
-23 = 6
Since the equation is not true, (0,-23) is not an ordered pair of the relation.
For (1,4), substitute x = 1 and y = 4 into the equation:
4 = (-2/3)(1) + 6
4 = -2/3 + 6
4 = 4 - 2/3
4 = 12/3 - 2/3
4 = 10/3
Since the equation is not true, (1,4) is not an ordered pair of the relation.
For (3,8), substitute x = 3 and y = 8 into the equation:
8 = (-2/3)(3) + 6
8 = -2 + 6
8 = 8
Since the equation is true, (3,8) is an ordered pair of the relation.
Therefore, the ordered pairs that are solutions to the equation y = -2/3x + 6 are (3,4) and (3,8).
To find the ordered pair(s) of a given relation, you need to substitute values for the variables and evaluate the equation. In this case, we have the relation given by y = -2/3x + 6.
To find the ordered pair(s), you can choose any value for x and calculate the corresponding value for y. Let's consider the options and evaluate them:
Option 1: (-3, 8)
Substituting x = -3 into the relation: y = -2/3(-3) + 6
Simplifying: y = 2 + 6 = 8
Option 2: (0, 6)
Substituting x = 0 into the relation: y = -2/3(0) + 6
Simplifying: y = 0 + 6 = 6
Option 3: (2, 3)
Substituting x = 2 into the relation: y = -2/3(2) + 6
Simplifying: y = -4/3 + 6 = 6 - 4/3 = 18/3 - 4/3 = 14/3 ≈ 4.67
Based on these evaluations, the ordered pair that satisfies the relation y = -2/3x + 6 is (2, 3).