Question

29b. three of the following represent the same relation. which representation does not match the others? circle the representation that does not match. a. $y = \frac{1}{2}x - 1$ b. graph c. one more than half of a number equals another number. d. \

$$\begin{tabular}{|c|c|} \\hline x & y \\\\ \\hline -2 & -2 \\\\ \\hline 0 & -1 \\\\ \\hline 4 & 1 \\\\ \\hline 10 & 4 \\\\ \\hline \\end{tabular}$$

Explanation:

Step1: Translate option C to equation

Let the first number be $x$, the second be $y$. The statement gives $y = \frac{1}{2}x + 1$.

Step2: Verify option A's equation

Option A is $y = \frac{1}{2}x - 1$.

Step3: Check option B's graph

The graph in B has a y-intercept of $-1$ and slope $\frac{1}{2}$, matching $y = \frac{1}{2}x - 1$.

Step4: Verify option D's table

Substitute $x$ values into $y = \frac{1}{2}x - 1$:

• $x=-2$: $y=\frac{1}{2}(-2)-1=-2$
• $x=0$: $y=\frac{1}{2}(0)-1=-1$
• $x=4$: $y=\frac{1}{2}(4)-1=1$
• $x=10$: $y=\frac{1}{2}(10)-1=4$

All match the table, so D fits $y = \frac{1}{2}x - 1$.

Step5: Compare all to find mismatch

Options A, B, D match $y = \frac{1}{2}x - 1$, while C matches $y = \frac{1}{2}x + 1$.

Answer:

C. One more than half of a number equals another number.