Question

i can use verbal descriptions to represent proportional relationships

1. it takes joe 12 minutes to ride a roller coaster four times. create a table to represent the relationship between the total time, y, and the number of rides, x.
2. write a situation to represent the equation y = 0.5x.
3. margie saves $15 of her allowance every two weeks. circle any of the following that represent the relationship between the total amount saved, y, and the number of weeks, x.

a.
weeks 1 2 3
$ saved 7.50 15 22.50
b. y = 7.5x
c. maggie will save $50 after 6 weeks
i can use a graph to represent proportional relationships.

1. lacey drives 125 miles and uses 5 gallons of gasoline. create a graph to represent the proportional relationship between the number of miles driven, y, and the amount of gasoline used, x.
2. sweet stuff is a baking company that bakes specialty cakes. sweet stuff can bake 6 cakes in 2 hours. create a graph to represent the relationship between y, the number of cakes baked, and x, the number of hours.

a. write an equation to represent y, the number of miles traveled on x number of gallons of gas.
b. how many gallons of gas are necessary to travel 350 miles?
a. write an equation to represent y, the number of cakes that can be baked in x hours.
b. in this situation, what does the ordered pair (4, 12) represent?

Explanation:

for Question 8:

Step1: Find time per ride

Time per ride = $\frac{12}{4} = 3$ minutes/ride

Step2: Define relationship

Total time $y = 3x$

Step3: Create table

Choose $x$ values (e.g., 0,1,2,3,4) and compute $y$:
$x=0$: $y=0$; $x=1$: $y=3$; $x=2$: $y=6$; $x=3$: $y=9$; $x=4$: $y=12$

Table for Question8:

Number of Rides ($x$)	0	1	2	3	4

for Question9:

Step1: Choose $x$ values

Pick $x=0,2,4$ (simplify decimals)

Step2: Compute $y$

$y=0.5x$ → $x=0$: $y=0$; $x=2$: $y=1$; $x=4$: $y=2$

Step3: Write solution

Solution: When $x$ is 0, $y$ is 0; $x$ is 2, $y$ is 1; $x$ is 4, $y$ is 2.

for Question10:

Step1: Find rate per week

Rate = $\frac{15}{2} = 7.5$ dollars/week

Step2: Check option A

Weeks=1: $7.5×1=7.5$; Weeks=2: $7.5×2=15$; Weeks=3: $7.5×3=22.5$ → matches

Step3: Check option B

Equation $y=7.5x$ → correct rate

Step4: Check option C

6 weeks: $7.5×6=45≠50$ → incorrect

for Question11a:

Step1: Find miles per gallon

Rate = $\frac{125}{5}=25$ miles/gallon

Step2: Write equation

$y=25x$

Answer:

for Question10:
A. (table), B. $y=7.5x$