Question

a) write an equation for the total cost of taking students and teachers to the skate
b) write the equation from part a in slope - intercept form.
unit 2 - item 10
create a story that models the graph below.
graph with distance from home on y - axis and time on x - axis, showing a piece - wise linear graph with a segment increasing, then flat, then increasing

Explanation:

Part A and B (Assuming Cost Details, e.g., Student Cost \( s \), Teacher Cost \( t \), Number of Students \( x \), Teachers \( y \))

A) Total Cost Equation

Step1: Define Variables

Let \( x \) = number of students, \( y \) = number of teachers, \( c_s \) = cost per student, \( c_t \) = cost per teacher.

Step2: Total Cost Formula

Total cost \( C = c_s x + c_t y \).
(If, e.g., \( c_s = 5 \), \( c_t = 10 \), then \( C = 5x + 10y \).)

B) Slope-Intercept Form (for a Single Variable, e.g., Solve for \( y \))

Step1: Start with Total Cost

\( C = 5x + 10y \) (using example values).

Step2: Solve for \( y \)

Subtract \( 5x \): \( 10y = -5x + C \).
Divide by 10: \( y = -\frac{1}{2}x + \frac{C}{10} \).

Unit 2 - Item 10: Story for the Graph

The graph has three segments: increasing (moving), flat (stopped), then increasing (moving faster). A story: "Alex starts walking from home to school at 3 mph. After 20 minutes (distance ~1 mile), they stop at a friend’s house for 10 minutes. Then they bike the rest of the way at 6 mph to reach school, increasing distance from home again."

Answer:

Story: "Alex departs home, walking slowly (distance from home rises). They pause at a friend’s house (distance stays same). Then they bike faster, so distance from home increases more steeply until reaching their destination (e.g., school)."

(Note: For Part A/B, specific numbers (e.g., costs, rates) were assumed as the problem’s original data was partial. Adjust variables/formulas to match given values if provided.)