List the ordered pairs obtained from the equation, given $\{-2,-1,0,1,2,3\}$ as the domain. Graph the set of ordered pairs. Give the range.

$y=-2 x+4$

How can the ordered pairs be found?
A. Substitute the values $-2,-1,0,1,2$, and 3 for $y$ in the equation and solve for x.
B. Substitute the values $-2,-1,0,1,2$, and 3 for $x$ in the equation and solve for $y$.
C. Substitute the values -2 and 3 for $x$ in the equation and solve for $y$.
D. Substitute the values -3 and 2 for $y$ in the equation and solve for $x$.

Substitute each value from the domain into the equation y = − 2 x + 4 to find the corresponding y-values.
List the ordered pairs: ( − 2 , 8 ) , ( − 1 , 6 ) , ( 0 , 4 ) , ( 1 , 2 ) , ( 2 , 0 ) , and ( 3 , − 2 ) .
Identify the range as the set of y-values: { − 2 , 0 , 2 , 4 , 6 , 8 } .
The correct method for finding the ordered pairs is to substitute x-values into the equation and solve for y, which is option B. Ordered pairs: ( − 2 , 8 ) , ( − 1 , 6 ) , ( 0 , 4 ) , ( 1 , 2 ) , ( 2 , 0 ) , ( 3 , − 2 ) ; Range: { − 2 , 0 , 2 , 4 , 6 , 8 } ; Method: B ​

Explanation

Understanding the Problem We are given the equation y = − 2 x + 4 and the domain { − 2 , − 1 , 0 , 1 , 2 , 3 } . We need to find the ordered pairs, graph them, determine the range, and choose the correct method for finding the ordered pairs.

Finding the Ordered Pairs To find the ordered pairs, we substitute each value from the domain into the equation y = − 2 x + 4 .

Calculating Ordered Pairs For x = − 2 , y = − 2 ( − 2 ) + 4 = 4 + 4 = 8 . So the ordered pair is ( − 2 , 8 ) .
For x = − 1 , y = − 2 ( − 1 ) + 4 = 2 + 4 = 6 . So the ordered pair is ( − 1 , 6 ) .
For x = 0 , y = − 2 ( 0 ) + 4 = 0 + 4 = 4 . So the ordered pair is ( 0 , 4 ) .
For x = 1 , y = − 2 ( 1 ) + 4 = − 2 + 4 = 2 . So the ordered pair is ( 1 , 2 ) .
For x = 2 , y = − 2 ( 2 ) + 4 = − 4 + 4 = 0 . So the ordered pair is ( 2 , 0 ) .
For x = 3 , y = − 2 ( 3 ) + 4 = − 6 + 4 = − 2 . So the ordered pair is ( 3 , − 2 ) .
The ordered pairs are ( − 2 , 8 ) , ( − 1 , 6 ) , ( 0 , 4 ) , ( 1 , 2 ) , ( 2 , 0 ) , and ( 3 , − 2 ) .

Determining the Range The range is the set of all y-values in the ordered pairs. The y-values are 8 , 6 , 4 , 2 , 0 , − 2 . So the range is { − 2 , 0 , 2 , 4 , 6 , 8 } .

Choosing the Correct Method The correct way to find the ordered pairs is to substitute the values from the domain (x-values) into the equation and solve for y. This corresponds to option B.


Examples
Understanding linear equations and ordered pairs is crucial in many real-world applications. For instance, imagine a taxi service that charges a fixed fee plus a per-mile rate. The equation y = − 2 x + 4 could represent a simplified version of this, where y is the total cost, x is the number of miles driven (with a negative coefficient indicating a discount or subsidy), and 4 is a base charge. By understanding how to generate ordered pairs and graph them, one can easily predict the cost for different distances and make informed decisions about transportation options. This concept extends to various scenarios involving rates, costs, and linear relationships.

Answered by GinnyAnswer | 2025-07-08

We found ordered pairs by substituting each x-value from the domain {-2, -1, 0, 1, 2, 3} into the equation y = − 2 x + 4 . The ordered pairs are ( − 2 , 8 ) , ( − 1 , 6 ) , ( 0 , 4 ) , ( 1 , 2 ) , ( 2 , 0 ) , ( 3 , − 2 ) , and the range is {8, 6, 4, 2, 0, -2}. The correct method is option B: substituting x-values to find corresponding y-values.
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Answered by Anonymous | 2025-07-22