Question

pottery class: ( y = 10x + 15 )

sessions	0	1	2	3	4
cost ($)	15	25	35	45	55

initial value for pottery class: 15
rate of change for pottery class: 10
find the initial value for the photography class.
initial value for photography class:
graph of photography class: x-axis (number of sessions) from 0 to 4, y-axis (total cost ($)) from 0 to 60, line passes through (0,0) etc.

Explanation:

Step1: Understand Initial Value

The initial value of a linear relationship (like the cost - session relationship here) is the value of \(y\) when \(x = 0\) (where \(x\) is the number of sessions and \(y\) is the total cost). For a graph, this is the \(y\)-intercept, i.e., the point where the line crosses the \(y\)-axis (when \(x=0\)).

Step2: Analyze the Graph

Looking at the graph for the photography class, when the number of sessions \(x = 0\) (the \(y\)-axis), the total cost \(y\) (from the graph) is \(0\) because the line passes through the origin \((0,0)\).

Answer:

\(0\)