Complete the table below for the equation [tex]y=-x+2[/tex]. Then use two of the ordered pairs to graph the equation.

| x | | y |
|---|---|---|
| -2| 4 | (-2,4)|
| -1| -1| (-1,3)|
| 0 | 2 | (0,2)|
| 1 | 1 | (1,1)|
| 2 | 0 | (2,0)

Substitute each given x value into the equation y = − x + 2 to calculate the corresponding y values.
Determine the ordered pairs ( − 2 , 4 ) , ( − 1 , 3 ) , ( 0 , 2 ) , ( 1 , 1 ) , and ( 2 , 0 ) .
Choose two ordered pairs, such as ( 0 , 2 ) and ( 2 , 0 ) , to plot on a coordinate plane.
Draw a straight line through the plotted points to represent the equation y = − x + 2 . The final answer is the completed table and the graph of the line. The y values are 4, 3, 2, 1, 0 for x values -2, -1, 0, 1, 2 respectively.

Explanation

Understanding the Problem We are given the equation y = − x + 2 and a table to complete with x values -2, -1, 0, 1, and 2. We need to find the corresponding y values for each x and then use two of the ordered pairs to graph the equation.

Calculating y values Let's find the y values for each given x value using the equation y = − x + 2 .


For x = − 2 :
y = − ( − 2 ) + 2 = 2 + 2 = 4 The ordered pair is ( − 2 , 4 ) .
For x = − 1 :
y = − ( − 1 ) + 2 = 1 + 2 = 3 The ordered pair is ( − 1 , 3 ) .
For x = 0 :
y = − ( 0 ) + 2 = 0 + 2 = 2 The ordered pair is ( 0 , 2 ) .
For x = 1 :
y = − ( 1 ) + 2 = − 1 + 2 = 1 The ordered pair is ( 1 , 1 ) .
For x = 2 :
y = − ( 2 ) + 2 = − 2 + 2 = 0 The ordered pair is ( 2 , 0 ) .

Choosing Ordered Pairs Now we have the following ordered pairs: ( − 2 , 4 ) , ( − 1 , 3 ) , ( 0 , 2 ) , ( 1 , 1 ) , and ( 2 , 0 ) . We can choose any two of these ordered pairs to graph the equation. Let's choose ( 0 , 2 ) and ( 2 , 0 ) . These points are easy to plot because they are the y-intercept and x-intercept, respectively.

Graphing the Equation Plot the points ( 0 , 2 ) and ( 2 , 0 ) on a coordinate plane. Draw a straight line that passes through both points. This line represents the equation y = − x + 2 .

Completed Table The completed table is:





x
y



-2
4


-1
3


0
2


1
1


2
0


Examples
Understanding linear equations like y = − x + 2 is crucial in many real-world scenarios. For instance, imagine you're selling lemonade. If each cup costs you $1 to make and you sell it for 2 , yo u r p ro f i t y c anb e m o d e l e d a s y = 2x - x , w h ere x i s t h e n u mb ero f c u p sso l d . T hi se q u a t i o nh e lp syo u d e t er min e h o w man yc u p syo u n ee d t ose llt ore a c ha cer t ain p ro f i t g o a l . S imi l a r l y , in p h ys i cs , t h ee q u a t i o n c an re p rese n tt h e m o t i o n o f an o bj ec t , w h ere y i s t h e p os i t i o nan d x$ is the time. By understanding the relationship between variables, you can predict future outcomes and make informed decisions.

Answered by GinnyAnswer | 2025-07-07

To complete the table for the equation y = − x + 2 , we substitute each given x value to find the corresponding y values. The ordered pairs we derive are ( − 2 , 4 ) , ( − 1 , 3 ) , ( 0 , 2 ) , ( 1 , 1 ) , ( 2 , 0 ) , and we can graph the equation using two of these points such as ( 0 , 2 ) and ( 2 , 0 ) . After graphing, we see a straight line reflecting the linear relationship of the equation.
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Answered by Anonymous | 2025-07-15