Which of the following represents a linear function with a slope of $\frac{1}{2}$ and a $y$ intercept of 3 ?
A. $3 x-9=6 y$
B. $f(x)$ increases by 2 units for every 1 unit $x$ increases, and $f(0)=3$
C
\begin{tabular}{|c|c|c|c|c|}
\hline$x$ & -10 & -8 & -6 & -4 \\
\hline$y$ & 8 & 7 & 6 & 5 \\
\hline
\end{tabular}
D. $-x+2 y=6$

Answer

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Answer

$\boxed{D. -x + 2y = 6}$

Steps

Step 1 ：Rewrite the given equations in the form y = mx + b

Step 2 ：Check if the slope m is $\frac{1}{2}$ and the y-intercept b is 3

Step 3 ：A: y = $\frac{1}{2}$x + $\frac{3}{2}$ (incorrect)

Step 4 ：B: slope is 2, not $\frac{1}{2}$ (incorrect)

Step 5 ：C: slope between points is -0.5, not $\frac{1}{2}$ (incorrect)

Step 6 ：D: y = $\frac{1}{2}$x + 3 (correct)

Step 7 ：$\boxed{D. -x + 2y = 6}$