Question

i can use tables to represent proportional relationships.

1. complete the table and sketch a graph of the relationship between the inches of rainfall, y, and the number of hours, x. then answer a - c.

a. what is the rate of change? explain its meaning in the context of the situation.
b. write an equation to represent the rainfall.
c. if the rainfall continues at this rate, how many inches of rain will fall after 6 hours?
i can write equations to represent proportional relationships.

1. an app developer projects that he will earn $20.00 for every 8 apps downloaded. write an equation to represent the proportional relationship between the total earnings, y, and the number of apps downloaded, x.
2. as the x - value increases by 3, the y - value increases by 12.

a. find the rate of change.
b. write an equation to represent the relationship between the x and y - values.

1. the table below shows the relationship between the total sales, y, and the number of textbooks sold, x.

a. what is the rate of change?
b. write an equation to represent the relationship.
7.

a. what is the rate of change?
b. write an equation to represent the relationship.

Explanation:

for Problem 3:

Step1: Complete the table

For x=1, y=3.5; x=2, y=7.0; x=4, y=14.0 (since 3.5×4=14).

Step2: Find rate of change (3a)

Rate = $\frac{\Delta y}{\Delta x} = \frac{7.0-3.5}{2-1} = 3.5$ in/hour.

Step3: Write equation (3b)

$y = 3.5x$.

Step4: Calculate rainfall at 6h (3c)

$y = 3.5×6 = 21$.

for Problem 4:

Step1: Find unit rate

Earnings per app: $\frac{20}{8} = 2.5$.

Step2: Write equation

$y = 2.5x$.

for Problem 5:

Step1: Find rate of change (5a)

Rate = $\frac{12}{3} = 4$.

Step2: Write equation (5b)

Assume proportionality: $y = 4x$.

for Problem 6:

Step1: Find rate of change (6a)

Rate = $\frac{64}{4} = 16$ dollars/textbook.

Step2: Write equation (6b)

$y = 16x$.

Answer:

3a. 3.5 inches per hour (rainfall increases by 3.5 inches each hour)
3b. $y = 3.5x$
3c. 21 inches

1. $y = 2.5x$

5a. 4
5b. $y = 4x$
6a. 16 dollars per textbook
6b. $y = 16x$
7a. 25 dollars per lawn
7b. $y = 25x$