Question

which table of values represents the equation $y = \frac{1}{2}x$?
first table (x, y):
2, 4
3, 6
5, 10
6, 12
second table (x, y):
2, 1
4, 2
7, 14
9, 18
third table (x, y):
1, $1\frac{1}{2}$
3, $3\frac{1}{2}$
4, $4\frac{1}{2}$
6, $6\frac{1}{2}$
fourth table (x, y):
1, $\frac{1}{2}$
4, 2
5, $2\frac{1}{2}$
8, 4

Explanation:

Step1: Recall the equation \( y = \frac{1}{2}x \)

We need to check for each table if \( y = \frac{1}{2}x \) holds for all given \( x \) and \( y \) values.

Step2: Check the first table

For \( x = 2 \), \( y = 4 \). Let's check \( \frac{1}{2}x=\frac{1}{2}\times2 = 1
eq4 \). So first table is incorrect.

Step3: Check the second table

For \( x = 2 \), \( y = 1 \). \( \frac{1}{2}\times2 = 1 \) (correct). For \( x = 4 \), \( y = 2 \). \( \frac{1}{2}\times4 = 2 \) (correct). For \( x = 7 \), \( y = 14 \). \( \frac{1}{2}\times7 = 3.5
eq14 \). So second table is incorrect.

Step4: Check the third table

For \( x = 1 \), \( y = 1\frac{1}{2}=\frac{3}{2} \). \( \frac{1}{2}\times1=\frac{1}{2}
eq\frac{3}{2} \). So third table is incorrect.

Step5: Check the fourth table

For \( x = 1 \), \( y=\frac{1}{2} \). \( \frac{1}{2}\times1=\frac{1}{2} \) (correct). For \( x = 4 \), \( y = 2 \). \( \frac{1}{2}\times4 = 2 \) (correct). For \( x = 5 \), \( y = 2\frac{1}{2}=\frac{5}{2} \). \( \frac{1}{2}\times5=\frac{5}{2} \) (correct). For \( x = 8 \), \( y = 4 \). \( \frac{1}{2}\times8 = 4 \) (correct). All values satisfy \( y=\frac{1}{2}x \).

Answer:

The fourth table (with \( x \) values 1, 4, 5, 8 and corresponding \( y \) values \( \frac{1}{2} \), 2, \( 2\frac{1}{2} \), 4)