Question

application
tony
tony has 2 dance moves down perfect, the robot and the centipede. every week he learns 3 new dance moves

1. what is the y-intercept?
2. what does the y-intercept mean?
3. what is the rate of change?
4. write the equation to model this.
5. graph this equation below.
6. how many dances move will tony have in 5 weeks? show steps to solve this!

toni
toni doesnt know any dance moves. she learns 5 moves every 2 weeks.
7 what is the initial value (start)? label it

1. what is the slope.
2. what does the slope mean?

(aka use your slope in a sentence with labels)

1. write the equation to model this.
2. graph this equation below.
3. when will toni have 20 dance moves?

show steps to solve this!
use the graph to answer the following:
mr. brust buys a box of candy canes. he eats them continuously. the graph models this situation.

1. what is the slope of the line?
2. what does the slope mean?

(aka use your slope in a sentence with labels)

1. what is the y-intercept?
2. what does the y-intercept mean in this situation?
3. what is the x-intercept?
4. what does the x-intercept mean in this situation?

Explanation:

Tony's Questions

Step1: Identify y-intercept (initial value)

The y-intercept is the starting number of dance moves, which is 2.

Step2: Interpret y-intercept

It represents Tony's starting dance moves.

Step3: Find rate of change (slope)

Tony learns 3 moves per week, so slope = 3.

Step4: Write linear equation

Use form $y=mx+b$, where $m=3$, $b=2$: $y=3x+2$

Step5: Graph the equation

• Plot y-intercept $(0, 2)$
• Use slope: from $(0,2)$, move 1 right, 3 up to $(1,5)$, draw line.

Step6: Calculate moves at 5 weeks

Substitute $x=5$ into $y=3x+2$:
$y=3(5)+2=15+2=17$

Toni's Questions

Step7: Identify initial value

Toni starts with 0 dance moves.

Step8: Calculate slope (rate of change)

Slope = $\frac{\text{change in moves}}{\text{change in weeks}}=\frac{5}{2}=2.5$

Step9: Interpret slope

Toni learns 2.5 dance moves per week.

Step10: Write linear equation

Use $y=mx+b$, $m=2.5$, $b=0$: $y=2.5x$

Step11: Graph the equation

• Plot y-intercept $(0,0)$
• Use slope: move 2 right, 5 up to $(2,5)$, draw line.

Step12: Solve for 20 dance moves

Set $y=20$, solve $20=2.5x$:
$x=\frac{20}{2.5}=8$

Mr. Brust's Candy Canes

Step13: Calculate slope

Use points $(0,6)$ and $(8,0)$:
$\text{slope}=\frac{0-6}{8-0}=-\frac{6}{8}=-\frac{3}{4}$

Step14: Interpret slope

Mr. Brust eats $\frac{3}{4}$ candy canes per minute.

Step15: Identify y-intercept

The y-intercept is 6 (when $x=0$).

Step16: Interpret y-intercept

Mr. Brust starts with 6 candy canes.

Step17: Identify x-intercept

The x-intercept is 8 (when $y=0$).

Step18: Interpret x-intercept

It takes 8 minutes to finish all candy canes.

Answer:

1. 2
2. Tony's starting number of dance moves.
3. 3
4. $y=3x+2$
5. (Graph with points (0,2) and (1,5), line connecting them)
6. 17
7. 0
8. $\frac{5}{2}$ or 2.5
9. Toni learns 2.5 dance moves per week.
10. $y=2.5x$ or $y=\frac{5}{2}x$
11. (Graph with points (0,0) and (2,5), line connecting them)
12. 8 weeks
13. $-\frac{3}{4}$
14. Mr. Brust eats $\frac{3}{4}$ candy canes per minute.
15. 6
16. Mr. Brust starts with 6 candy canes.
17. 8
18. It takes 8 minutes for Mr. Brust to eat all his candy canes.