Question

which of the following tables represents a linear relationship that is also proportional?
1.
$\boldsymbol{x}$ -1 2 5
$\boldsymbol{y}$ -1 0 1
2.
$\boldsymbol{x}$ -2 -1 0
$\boldsymbol{y}$ -1 0 1
3.
$\boldsymbol{x}$ -2 -1 0
$\boldsymbol{y}$ -4 -2 0
4.
$\boldsymbol{x}$ -4 -2 1
$\boldsymbol{y}$ -2 0 3

Explanation:

Step1: Define proportional linear relation

A proportional linear relationship follows $y = kx$ (passes through origin, $\frac{y}{x}$ is constant for all $x
eq0$).

Step2: Check first table

Calculate $\frac{y}{x}$: $\frac{-1}{-1}=1$, $\frac{0}{2}=0$, $\frac{1}{5}=0.2$. Not constant.

Step3: Check second table

Calculate $\frac{y}{x}$: $\frac{-1}{-2}=0.5$, $\frac{0}{-1}=0$, $\frac{1}{0}$ undefined. Not constant.

Step4: Check third table

Calculate $\frac{y}{x}$: $\frac{-4}{-2}=2$, $\frac{-2}{-1}=2$, $\frac{0}{0}$ (origin included). Constant $k=2$, follows $y=2x$.

Step5: Check fourth table

Calculate $\frac{y}{x}$: $\frac{-2}{-4}=0.5$, $\frac{0}{-2}=0$, $\frac{3}{1}=3$. Not constant.

Answer:

The table:

x	-2	-1	0