Question

constant of proportionality - table
the values of $x$ and $y$ are proportional. determine the constant of proportionality($k$) and find the missing values.
1)
2)
3)
4)
5)
6)
7)
8)

Explanation:

1)

Step1: Find k from known pair

$k = \frac{y}{x} = \frac{36}{9} = 4$

Step2: Find missing x for y=16

$x = \frac{y}{k} = \frac{16}{4} = 4$

Step3: Find y for x=5

$y = kx = 4\times5 = 20$

Step4: Find missing x for y=8

$x = \frac{y}{k} = \frac{8}{4} = 2$

2)

Step1: Find k from known pair

$k = \frac{y}{x} = \frac{2}{6} = \frac{1}{3}$

Step2: Find missing x for y=4

$x = \frac{y}{k} = \frac{4}{\frac{1}{3}} = 12$

Step3: Find y for x=15

$y = kx = \frac{1}{3}\times15 = 5$

Step4: Find y for x=9

$y = kx = \frac{1}{3}\times9 = 3$

3)

Step1: Find k from known pair

$k = \frac{y}{x} = \frac{8}{48} = \frac{1}{6}$

Step2: Find y for x=12

$y = kx = \frac{1}{6}\times12 = 2$

Step3: Find missing x for y=3

$x = \frac{y}{k} = \frac{3}{\frac{1}{6}} = 18$

Step4: Find y for x=30

$y = kx = \frac{1}{6}\times30 = 5$

4)

Step1: Find k from known pair

$k = \frac{y}{x} = \frac{20}{4} = 5$

Step2: Find missing x for y=25

$x = \frac{y}{k} = \frac{25}{5} = 5$

Step3: Find missing x for y=40

$x = \frac{y}{k} = \frac{40}{5} = 8$

Step4: Find missing x for y=60

$x = \frac{y}{k} = \frac{60}{5} = 12$

5)

Step1: Find k from known pair

$k = \frac{y}{x} = \frac{32}{4} = 8$

Step2: Find y for x=7

$y = kx = 8\times7 = 56$

Step3: Find y for x=11

$y = kx = 8\times11 = 88$

Step4: Find missing x for y=24

$x = \frac{y}{k} = \frac{24}{8} = 3$

6)

Step1: Find k from known pair

$k = \frac{y}{x} = \frac{6}{14} = \frac{3}{7}$

Step2: Find missing x for y=21

$x = \frac{y}{k} = \frac{21}{\frac{3}{7}} = 49$

Step3: Find missing x for y=15

$x = \frac{y}{k} = \frac{15}{\frac{3}{7}} = 35$

Step4: Find missing x for y=3

$x = \frac{y}{k} = \frac{3}{\frac{3}{7}} = 7$

7)

Step1: Find k from known pair

$k = \frac{y}{x} = \frac{12}{30} = \frac{2}{5}$

Step2: Find missing x for y=14

$x = \frac{y}{k} = \frac{14}{\frac{2}{5}} = 35$

Step3: Find y for x=5

$y = kx = \frac{2}{5}\times5 = 2$

Step4: Find missing x for y=6

$x = \frac{y}{k} = \frac{6}{\frac{2}{5}} = 15$

8)

Step1: Find k from known pair

$k = \frac{y}{x} = \frac{18}{3} = 6$

Step2: Find y for x=4

$y = kx = 6\times4 = 24$

Step3: Find missing x for y=54

$x = \frac{y}{k} = \frac{54}{6} = 9$

Step4: Find y for x=7

$y = kx = 6\times7 = 42$

Answer:

1. Constant $k=4$; missing values: $x=4$, $y=20$, $x=2$
2. Constant $k=\frac{1}{3}$; missing values: $x=12$, $y=5$, $y=3$
3. Constant $k=\frac{1}{6}$; missing values: $y=2$, $x=18$, $y=5$
4. Constant $k=5$; missing values: $x=5$, $x=8$, $x=12$
5. Constant $k=8$; missing values: $y=56$, $y=88$, $x=3$
6. Constant $k=\frac{3}{7}$; missing values: $x=49$, $x=35$, $x=7$
7. Constant $k=\frac{2}{5}$; missing values: $x=35$, $y=2$, $x=15$
8. Constant $k=6$; missing values: $y=24$, $x=9$, $y=42$