Question

Write an equation in function notation for this relation.

Short answer

The equation in function notation for this relation is$y=3x$.

Step-by-step solution

Step 1. Find the points from the graph and make the table and find the difference between the values of x and y.

The observed points from the graph are $\left(-2,-6\right),\left(-1,-3\right),\left(0,0\right),\left(1,3\right),\left(2,6\right)$and $\left(3,9\right)$.

Make the table by using the observed points from the graph.

x	$-2$	$-1$	0	1	2	3
y	$-6$	$-3$	0	3	6	9

Calculate the difference between and.

From the above table it can be noticed that the difference between x is 1 and the difference between the y is 3.

This implies the value of constant of variation (k) is given by:

$$\begin{gathered} k=\frac{3}{1} \\ =3 \end{gathered}$$

Step 2. Find the equation in function notation for this relation.

As, the value of k is 3. Therefore, the equation in function notation for this relation is given by:

$\begin{array}{c}y=kx\\ y=3x\end{array}$

Therefore, the equation in function notation for this relation is $y=3x$.