Final Answer:
The table matches each ordered pair to its corresponding equation by checking which equation is satisfied when the x- and y-values of the pair are substituted.
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Explanation:
We need to verify that each ordered pair (x, y) satisfies the given equation in the same row. That means plugging the x-value into the equation and seeing if we get the y-value.
Let’s check a few to see how it works:
1. Pair: (−3, 0), Equation: y = 0
Plug x = −3 into y = 0 → y = 0. The pair has y = 0, so it matches.
2. Pair: (3, 0), Equation: y = −x + 3
Plug x = 3: y = −3 + 3 = 0. The pair has y = 0 → matches.
3. Pair: (−1, 2), Equation: y = ½x + 2.5
Plug x = −1: y = ½(−1) + 2.5 = −0.5 + 2.5 = 2. The pair has y = 2 → matches.
4. Pair: (2, 3), Equation: x = 2
This equation says x must be 2 — and the pair has x = 2. y can be anything, and here y = 3, so it’s fine.
5. Pair: (0, −2), Equation: y = −½x − 2
Plug x = 0: y = −½(0) − 2 = −2. Pair has y = −2 → matches.
We do this for every row — substitute x into the right side of the equation and see if it gives the y from the pair. All rows in the table are correctly matched.
So the table is already correct as given.
Parent Tip: Review the logic above to help your child master the concept of writing equations in slope intercept form given two points worksheet.
