Question

table
x | y
0 | 0
1 |
2 |
3 |
4 |
constant of proportionality
equation
write your own question & answer.

Explanation:

Step1: Identify the relationship

We check the ratio of \( y \) to \( x \) for each non - zero \( x \). For \( x = 1\), \( y = 2\) (assuming the first non - zero \( y \) is 2, maybe a typo in the image but following proportionality). For \( x = 2\), if \( y = 4\), the ratio \( \frac{y}{x}=\frac{4}{2} = 2\). For \( x = 3\), if \( y = 6\) (assuming), \( \frac{y}{x}=\frac{6}{3}=2\), for \( x = 4\), \( \frac{y}{x}=\frac{8}{4} = 2\) (assuming the pattern). The constant of proportionality \( k=\frac{y}{x}\).

Step2: Calculate the constant

Using the formula for constant of proportionality \( k=\frac{y}{x}\). Taking \( x = 2\) and \( y = 4\), \( k=\frac{4}{2}=2\).

Step3: Write the equation

The equation for a proportional relationship is \( y=kx\). Since \( k = 2\), the equation is \( y = 2x\).

Answer:

Constant of Proportionality: \( 2 \)
Equation: \( y = 2x \)