Which two points are in the solution set of y > -x + 3?
Understand the Problem
The question asks which two points from a given set satisfy the inequality y > -x + 3. To solve this, we will evaluate each point by substituting the x-value into the equation and determining if the resulting y-value is greater than the computed value.
Answer
The two points are $(2, 4)$ and $(6, 0)$.
Answer for screen readers
The two points that satisfy the inequality $y > -x + 3$ are $(2, 4)$ and $(6, 0)$.
Steps to Solve
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Identify the Inequality We are given the inequality $y > -x + 3$. This means we need to find points $(x, y)$ that lie above the line represented by the equation $y = -x + 3$.
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Evaluate the Given Points We will substitute the x-values of each point into the equation $y = -x + 3$ and compare the computed y-value with the y-value of the point.
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For point $(-2, 3)$: $$ y = -(-2) + 3 = 2 + 3 = 5 $$ Check: $3 > 5$ (False)
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For point $(2, 4)$: $$ y = -(2) + 3 = -2 + 3 = 1 $$ Check: $4 > 1$ (True)
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For point $(6, 0)$: $$ y = -(6) + 3 = -6 + 3 = -3 $$ Check: $0 > -3$ (True)
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For point $(0, 3)$: $$ y = -(0) + 3 = 0 + 3 = 3 $$ Check: $3 > 3$ (False)
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Identify Valid Points From the evaluations, the points that satisfy the inequality are $(2, 4)$ and $(6, 0)$.
The two points that satisfy the inequality $y > -x + 3$ are $(2, 4)$ and $(6, 0)$.
More Information
In this problem, we assessed whether points lie above a linear boundary defined by the inequality. Understanding inequalities helps in graphing and determining the region of solutions in coordinate geometry.
Tips
- Not evaluating the correct inequality: Ensure to compare the computed y-value correctly with the point's y-value.
- Misinterpreting "greater than": Remember that "greater than" means the actual y-value must be strictly more than the calculated value.
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