Question

which of the following tables represents a linear relationship that is also proportional?

x	y
4	4
8	6

x	y
2	1
4	2

x	y
5	3
10	5

Explanation:

Step1: Define proportional linearity

A proportional linear relationship follows $y=kx$ (passes through $(0,0)$ and has constant $\frac{y}{x}$ for $x
eq0$).

Step2: Check Table 1

Table1: $(0,2)$ does not satisfy $y=kx$ (since $2
eq k*0$). Reject.

Step3: Check Table 2

Table2: $(0,0)$ fits. Calculate $\frac{y}{x}$:
$\frac{1}{2}=0.5$, $\frac{2}{4}=0.5$. Constant ratio, linear.

Step4: Check Table 3

Table3: $(0,1)$ does not satisfy $y=kx$ (since $1
eq k*0$). Reject.

Answer:

The second table:

x	y
2	1
4	2