Question

at the left you can see 4 clusters of circles with the number of circles in each cluster written below it. determine if the function s(x) that maps the cluster to its number of circles is a linear function. if it is linear, find the equation of the function s(x). s(1)=8 s(2)=13 s(3)=20 s(4)=29
□ s(x) is not a linear function
s(x)=□

Explanation:

Step1: Check the slope between points

For a linear function $y = mx + b$, the slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
Let $(x_1,y_1)=(1,8)$ and $(x_2,y_2)=(2,13)$. Then $m_1=\frac{13 - 8}{2 - 1}=5$.
Let $(x_1,y_1)=(2,13)$ and $(x_2,y_2)=(3,20)$. Then $m_2=\frac{20 - 13}{3 - 2}=7$.
Since $m_1
eq m_2$, the function is not linear.

Answer:

$s(x)$ is not a linear function