Question

i can use tables to represent proportional relationships. 3. 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?

Explanation:

Step1: Find the rate of change

The rate of change (slope) \(m\) for a proportional relationship \(y = mx\) can be found using the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points \((x_1,y_1)=(1,3.5)\) and \((x_2,y_2)=(3,10.5)\). Then \(m=\frac{10.5 - 3.5}{3 - 1}=\frac{7}{2}=3.5\).
In the context of the situation, it means that the amount of rainfall increases by \(3.5\) inches per hour.

Step2: Write the equation

Since the relationship is proportional \(y = mx\), and \(m = 3.5\), the equation is \(y=3.5x\).

Step3: Find the rainfall after 6 hours

Substitute \(x = 6\) into the equation \(y=3.5x\). So \(y=3.5\times6 = 21\).

Answer:

a. The rate of change is \(3.5\). It means the rainfall increases by \(3.5\) inches each hour.
b. The equation is \(y = 3.5x\).
c. After 6 hours, \(21\) inches of rain will fall.