Math Problem Statement
Which equation describes the relation indicated by the table? The table lists four values of x and their corresponding y values: (-2, 3), (0, 2), (4, 0), and (6, -1), and four possible equations: A: y = -x + 1, B: y = x/2 - 2, C: y = -x + 2, D: y = -x/2 + 2.
Solution
Let's analyze the table and check which equation matches the relationship.
The table provides values for and :
\hline x & y \\ \hline -2 & 3 \\ 0 & 2 \\ 4 & 0 \\ 6 & -1 \\ \hline \end{array}$$ We are given four equations to choose from: - $$A: y = -x + 1$$ - $$B: y = \frac{x}{2} - 2$$ - $$C: y = -x + 2$$ - $$D: y = -\frac{x}{2} + 2$$ ### Step 1: Check Equation A ($$y = -x + 1$$) - For $$x = -2$$, $$y = -(-2) + 1 = 2 + 1 = 3$$ (Correct) - For $$x = 0$$, $$y = -(0) + 1 = 1$$ (Incorrect) This is not the correct equation. ### Step 2: Check Equation B ($$y = \frac{x}{2} - 2$$) - For $$x = -2$$, $$y = \frac{-2}{2} - 2 = -1 - 2 = -3$$ (Incorrect) This is not the correct equation. ### Step 3: Check Equation C ($$y = -x + 2$$) - For $$x = -2$$, $$y = -(-2) + 2 = 2 + 2 = 4$$ (Incorrect) This is not the correct equation. ### Step 4: Check Equation D ($$y = -\frac{x}{2} + 2$$) - For $$x = -2$$, $$y = -\frac{-2}{2} + 2 = 1 + 2 = 3$$ (Correct) - For $$x = 0$$, $$y = -\frac{0}{2} + 2 = 0 + 2 = 2$$ (Correct) - For $$x = 4$$, $$y = -\frac{4}{2} + 2 = -2 + 2 = 0$$ (Correct) - For $$x = 6$$, $$y = -\frac{6}{2} + 2 = -3 + 2 = -1$$ (Correct) ### Conclusion: The correct equation is **D: $$y = -\frac{x}{2} + 2$$**. Would you like further details or have any questions? ### Related Questions: 1. How can we derive the slope of a line from a table of values? 2. What is the difference between a positive and negative slope? 3. How can we check the y-intercept of a line using a table? 4. How do you interpret fractional slopes like $$-\frac{1}{2}$$? 5. What are the steps to convert a table of values into a linear equation? **Tip**: Always test each given equation with all the points in the table to verify which one fits best.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Formulas
Slope-intercept form: y = mx + b
Theorems
Slope of a line
Point-slope relationship
Suitable Grade Level
Grades 8-10
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