Question

what is the constant of proportionality in this proportional relationship?

x	2	$2\frac{1}{2}$	3	$3\frac{1}{2}$
y	$\frac{5}{2}$	$\frac{25}{8}$	$\frac{15}{4}$	$\frac{35}{8}$

• $\frac{4}{5}$
• $\frac{5}{4}$
• 4
• 5

Explanation:

Step1: Recall proportionality formula

For a proportional relationship, $y = kx$, so $k = \frac{y}{x}$.

Step2: Calculate k using first pair

Use $x=2$, $y=\frac{5}{2}$:
$k = \frac{\frac{5}{2}}{2} = \frac{5}{2} \times \frac{1}{2} = \frac{5}{4}$

Step3: Verify with second pair

Use $x=2\frac{1}{2}=\frac{5}{2}$, $y=\frac{25}{8}$:
$k = \frac{\frac{25}{8}}{\frac{5}{2}} = \frac{25}{8} \times \frac{2}{5} = \frac{5}{4}$

Step4: Verify with third pair

Use $x=3$, $y=\frac{15}{4}$:
$k = \frac{\frac{15}{4}}{3} = \frac{15}{4} \times \frac{1}{3} = \frac{5}{4}$

Step5: Verify with fourth pair

Use $x=3\frac{1}{2}=\frac{7}{2}$, $y=\frac{35}{8}$:
$k = \frac{\frac{35}{8}}{\frac{7}{2}} = \frac{35}{8} \times \frac{2}{7} = \frac{5}{4}$

Answer:

$\boldsymbol{\frac{5}{4}}$ (corresponding to the second option)