Question

the student center also offers a photography class. the graph shows the total cost of a class, y, as a function of the number of sessions attended, x.
pottery class: y = 10x + 15
sessions | cost ($)
0 | 15
1 | 25
2 | 35
3 | 45
4 | 55
complete the table for photography:
sessions | cost ($)
0 | 0
1 | 15
2 | 30
3 | 45
4 | 60
when does the photography class cost less? choose all that apply.
1 session
2 sessions
3 sessions
4 sessions

Explanation:

Step1: Analyze Photography Class Cost

From the graph, the Photography Class has a point (1, 15), so its cost function is \( y = 15x \) (since it passes through the origin, slope is \( \frac{15 - 0}{1 - 0}=15 \)).

Step2: Analyze Pottery Class Cost

Pottery Class cost function is \( y = 10x + 15 \).

Step3: Compare Costs for Each Session

• 1 session:

Photography: \( y = 15(1) = 15 \)
Pottery: \( y = 10(1) + 15 = 25 \)
Photography is cheaper.

• 2 sessions:

Photography: \( y = 15(2) = 30 \)
Pottery: \( y = 10(2) + 15 = 35 \)
Photography is cheaper.

• 3 sessions:

Photography: \( y = 15(3) = 45 \)
Pottery: \( y = 10(3) + 15 = 45 \)
Equal cost.

• 4 sessions:

Photography: \( y = 15(4) = 60 \)
Pottery: \( y = 10(4) + 15 = 55 \)
Pottery is cheaper.

Answer:

1 session, 2 sessions