Question

1. what is the constant rate of change of the table below?

hours: 2, 4, 6, 8
miles: 70, 140, 210, 280
a. 105 miles per hour
c. 50 miles per hour
b. 70 miles per hour
d. 35 miles per hour

1. what is the slope of the line?

(graph: amount of water vs numbers of plants, line from (0,0) with points)
f. \\(\frac{1}{2}\\)
g. 2
h. 5
i. 12

1. dawson rakes leaves in his neighborhood. the equation \\(y = 10x\\) represents the amount of money he earns. what is the constant of proportionality?

a. 1
c. 10
b. 5
d. 20

1. what is the solution of the proportion \\(\frac{3}{16} = \frac{9}{y}\\)?

f. 32
g. 48
h. 60

Explanation:

Step1: Calculate rate of change (Q1)

$\text{Rate} = \frac{140-70}{4-2} = \frac{70}{2} = 35$

Step2: Calculate slope (Q2)

Use points $(2,1)$: $\text{Slope} = \frac{1-0}{2-0} = \frac{1}{2}$

Step3: Identify proportionality constant (Q3)

For $y=kx$, $k=10$

Step4: Solve proportion (Q4)

Cross multiply: $3y=16 \times 9 \implies y=\frac{144}{3}=48$

Answer:

1. D. 35 miles per hour
2. F. $\frac{1}{2}$
3. C. 10
4. G. 48