Question

which equation represents the relationship between x and y shown in the table?

x	y
2	1
4	5
6	9
8	13

options: $y = \frac{1}{2}x + 4$, $y = \frac{1}{2}x - 4$, $y = 2x - 3$, $y = 2x + 1$

Explanation:

Step1: Test first pair in equations

Test $x=2, y=1$:

• $y=\frac{1}{2}x+4$: $\frac{1}{2}(2)+4=1+4=5

eq1$

• $y=\frac{1}{2}x-4$: $\frac{1}{2}(2)-4=1-4=-3

eq1$

• $y=2x-3$: $2(2)-3=4-3=1$ (matches)
• $y=2x+1$: $2(2)+1=4+1=5

eq1$

Step2: Verify with second pair

Test $x=4, y=5$ in $y=2x-3$:
$2(4)-3=8-3=5$ (matches)

Step3: Verify third pair

Test $x=6, y=9$ in $y=2x-3$:
$2(6)-3=12-3=9$ (matches)

Step4: Verify fourth pair

Test $x=8, y=13$ in $y=2x-3$:
$2(8)-3=16-3=13$ (matches)

Answer:

$y=2x-3$