Math Problem Statement
Which table of values represents a linear function? A xx yy minus, 1−1 77 11 33 33 minus, 1−1 55 minus, 5−5 B xx yy minus, 6−6 minus, 6−6 minus, 2−2 minus, 4−4 22 minus, 2−2 66 11 C xx yy minus, 4−4 44 minus, 1−1 22 33 00 77 minus, 2−2 D xx yy 11 33 33 55 55 66 77 88 Answer
Solution
To determine which table of values represents a linear function, we need to check if the relationship between and in the table follows the pattern of a linear equation, which has the form , where is the slope.
Checking each table:
Table A:
\hline x & y \\ \hline -1 & 7 \\ 1 & 3 \\ 3 & -1 \\ 5 & -5 \\ \hline \end{array}$$ - Differences in $$x$$: $$1 - (-1) = 2$$, $$3 - 1 = 2$$, $$5 - 3 = 2$$ - Differences in $$y$$: $$3 - 7 = -4$$, $$-1 - 3 = -4$$, $$-5 - (-1) = -4$$ Since the differences in $$x$$ and $$y$$ are consistent, this indicates a constant rate of change, meaning the function is linear. #### Table B: $$\begin{array}{|c|c|} \hline x & y \\ \hline -6 & -6 \\ -2 & -4 \\ 2 & -2 \\ 6 & 1 \\ \hline \end{array}$$ - Differences in $$x$$: $$-2 - (-6) = 4$$, $$2 - (-2) = 4$$, $$6 - 2 = 4$$ - Differences in $$y$$: $$-4 - (-6) = 2$$, $$-2 - (-4) = 2$$, $$1 - (-2) = 3$$ The differences in $$y$$ are not consistent, so this function is not linear. #### Table C: $$\begin{array}{|c|c|} \hline x & y \\ \hline -4 & 4 \\ -1 & 2 \\ 3 & 0 \\ 7 & -2 \\ \hline \end{array}$$ - Differences in $$x$$: $$-1 - (-4) = 3$$, $$3 - (-1) = 4$$, $$7 - 3 = 4$$ - Differences in $$y$$: $$2 - 4 = -2$$, $$0 - 2 = -2$$, $$-2 - 0 = -2$$ The differences in $$x$$ are not consistent, so this function is not linear. #### Table D: $$\begin{array}{|c|c|} \hline x & y \\ \hline 1 & 3 \\ 3 & 5 \\ 5 & 6 \\ 7 & 8 \\ \hline \end{array}$$ - Differences in $$x$$: $$3 - 1 = 2$$, $$5 - 3 = 2$$, $$7 - 5 = 2$$ - Differences in $$y$$: $$5 - 3 = 2$$, $$6 - 5 = 1$$, $$8 - 6 = 2$$ The differences in $$y$$ are not consistent, so this function is not linear. ### Conclusion: The table that represents a linear function is **Table A** because both the differences in $$x$$ and $$y$$ are consistent. Do you want details or have any questions? --- **Related Questions:** 1. How do you calculate the slope from a table of values? 2. What is the equation of the linear function from Table A? 3. Can a nonlinear function ever have consistent differences in $$x$$? 4. How do you know if a table represents an exponential function? 5. How do you find the y-intercept of a function from a table? **Tip:** A linear function always has a constant rate of change in both $$x$$ and $$y$$.Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Linear Functions
Rate of Change
Formulas
Linear equation: y = mx + b
Theorems
-
Suitable Grade Level
Grades 7-9