Question

pottery class: y = 10x + 15
sessions | 0 | 1 | 2 | 3 | 4
cost ($) | 15 | 25 | 35 | 45 | 55
initial value for pottery class: 15
rate of change for pottery class: 10
find the rate of change for the
photography class.
rate of change for photography class:
graph of photography class with x-axis number of sess, y-axis total cost ($), line from (0,0) upwards

Explanation:

Step1: Recall rate of change formula

The rate of change (slope) of a linear function is given by $\frac{\Delta y}{\Delta x}$, where $\Delta y$ is the change in $y$ (total cost) and $\Delta x$ is the change in $x$ (number of sessions).

Step2: Identify two points on the graph

From the graph of the photography class, when $x = 0$, $y = 0$ (the line passes through the origin). Let's take another point. For example, when $x = 3$, let's find $y$. Looking at the grid, each square seems to represent 1 unit on $x$ and 15 units? Wait, no, let's check the axes. The $y$-axis is total cost in dollars, $x$-axis is number of sessions. Let's take two points: (0, 0) and (3, 45)? Wait, no, wait the line: when $x = 3$, what's $y$? Wait, the grid: each horizontal line is 15, 30, 45, 60. Each vertical line is 0,1,2,3,4,5,6. Wait, let's take (3, 45)? No, wait the line: from (0,0) to (3, 45)? Wait, no, maybe (1, 15)? Wait, no, let's check the slope. Wait, the line goes through (0,0) and let's see, when $x = 3$, $y = 45$? Wait, no, the grid: each square is, say, $x$ increases by 1, $y$ increases by 15? Wait, no, let's calculate the slope. Let's take two points: (0, 0) and (2, 30). Wait, when $x=2$, $y=30$? Wait, no, the graph: the line for photography class. Let's take (0,0) and (3, 45). Then $\Delta y = 45 - 0 = 45$, $\Delta x = 3 - 0 = 3$. Then slope is $\frac{45}{3} = 15$. Wait, or (1, 15) and (2, 30). Then $\Delta y = 30 - 15 = 15$, $\Delta x = 2 - 1 = 1$. So slope is $\frac{15}{1} = 15$. So the rate of change is 15.

Wait, let's confirm. The formula for rate of change (slope) is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points on the photography class line. From the graph, when $x = 0$, $y = 0$ (point (0,0)). When $x = 1$, what's $y$? Looking at the graph, the line passes through (1, 15)? Wait, no, the grid: the $y$-axis has 15, 30, 45, 60. So each horizontal line is 15 units. So when $x = 1$, $y = 15$? Wait, no, the line: from (0,0) to (1, 15), (2, 30), (3, 45), etc. So the change in $y$ when $x$ increases by 1 is 15. So the rate of change is $\frac{15 - 0}{1 - 0} = 15$. So the rate of change is 15.

Answer:

15