Question

Determine whether each table or graph represents a proportional

Answer 1

Answer:

Table 2 and  3 represent a proportional relationship because the ratio between two variables are equivalent.

Step-by-step explanation:

If variable y is proportional to variable x, then

$y\propto x$

$y=kx$

$\frac{y}{x}=k$

where k is constant of proportionality.

For table 1,

$\dfrac{y_1}{x_1}=\dfrac{5}{1}$

$\dfrac{y_2}{x_2}=\dfrac{9}{2}$

$\dfrac{5}{1}\neq \dfrac{9}{2}$

Therefore, table 1 does not represents a proportional relationship.

Similarly

For table 2,

$\dfrac{\frac{7}{2}}{1}=\dfrac{\frac{21}{2}}{3}=\dfrac{\frac{35}{2}}{5}=\dfrac{\frac{49}{2}}{7}=\dfrac{\frac{63}{2}}{9}=\frac{7}{2}$

All ratios are equivalent, therefore Table 2 represents a proportional relationship.

For table 3,

$\dfrac{110}{2}=\dfrac{275}{5}=\dfrac{495}{9}=\dfrac{770}{14}=55$

All ratios are equivalent, therefore Table 3 represents a proportional relationship.

For table 4,

$\dfrac{29.25}{3}=\dfrac{48.75}{5}\neq \dfrac{74}{8}$

All ratios are not equivalent, therefore Table 4 does not represent a proportional relationship.

Answer 2

Answer:

1. not proportional because it's increasing in different values

2. proportional because the value is increasing equally

3. proportional because the values are increasing in equal amount

4. Proportional because it's increasing in equal amounts