Math Problem Statement
Which students correctly wrote an equation to represent the function based on the given table of values?
Solution
The problem asks which student(s) correctly wrote an equation to represent the linear function, based on the given table of values.
Table of values:
x & y \\ \hline 1 & 5 \\ 2 & 7 \\ -2 & -1 \\ \end{array}$$ The three students proposed the following equations: - **Kecie**: $$y = 5 + 3(x - 1)$$ - **Taylor**: $$y = 3x - 2$$ - **Desmond**: $$3x - y = -2$$ Let's analyze them step by step. ### Step 1: Identify the slope of the function. The values of $$y$$ increase by 2 when $$x$$ increases by 1, which indicates the slope $$m = 2$$. ### Step 2: Find the equation of the line. We can use the point-slope form of the equation $$y - y_1 = m(x - x_1)$$, where $$m = 2$$ and $$(x_1, y_1) = (1, 5)$$ is one of the points. Substituting into the point-slope form: $$y - 5 = 2(x - 1)$$ Simplifying: $$y = 2(x - 1) + 5 y = 2x - 2 + 5 y = 2x + 3$$ ### Step 3: Check each student's equation. - **Kecie**: $$y = 5 + 3(x - 1)$$ is incorrect because the slope should be 2, not 3. - **Taylor**: $$y = 3x - 2$$ is incorrect because the slope should be 2, and the constant term is wrong. - **Desmond**: $$3x - y = -2$$ simplifies to $$y = 3x + 2$$, which also has the wrong slope (3 instead of 2). ### Conclusion: None of the students wrote the correct equation. The correct equation is $$y = 2x + 3$$, which none of them presented. Let me know if you want more details or explanations. ### Follow-up questions: 1. How is the slope determined from a table of values? 2. What is the point-slope form of a linear equation, and when is it used? 3. How do you convert the point-slope form into slope-intercept form? 4. Why is it important to use a specific point from the table when writing the equation of a line? 5. What mistakes are common when interpreting the slope and intercept from an equation? ### Tip: When working with tables of linear functions, always check how the $$y$$-values change with respect to $$x$$ to find the slope.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Functions
Slope-Intercept Form
Point-Slope Form
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Point-slope form: y - y1 = m(x - x1)
Slope-intercept form: y = mx + b
Theorems
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Suitable Grade Level
Grades 8-10