eureka math grade 4 lesson 8 homework 4 5

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Eureka Math Grade 8 Module 4 Lesson 22 Answer Key

Engage ny eureka math 8th grade module 4 lesson 22 answer key, eureka math grade 8 module 4 lesson 22 exercise answer key.

Exercise 1. Peter paints a wall at a constant rate of 2 square feet per minute. Assume he paints an area y, in square feet, after x minutes. a. Express this situation as a linear equation in two variables. Answer: \(\frac{y}{x}\) = \(\frac{2}{1}\) y = 2x

c. Using the graph or the equation, determine the total area he paints after 8 minutes, 1 \(\frac{1}{2}\) hours, and 2 hours. Note that the units are in minutes and hours. Answer: In 8 minutes, he paints 16 square feet. y = 2(90) = 180

In 1 \(\frac{1}{2}\) hours, he paints 180 square feet. y = 2(120) = 240

In 2 hours, he paints 240 square feet.

b. Who walks at a greater speed? Explain. Answer: Nathan walks at a greater speed. The slope of the graph for Nathan is 4, and the slope or rate for Nicole is \(\frac{25}{7}\). When you compare the slopes, you see that 4 > \(\frac{25}{7}\).

Exercise 3. a. Susan can type 4 pages of text in 10 minutes. Assuming she types at a constant rate, write the linear equation that represents the situation. Answer: Let y represent the total number of pages Susan can type in x minutes. We can write \(\frac{y}{x}\) = \(\frac{4}{10}\) and y = \(\frac{2}{5}\) x.

Exercise 4. a. Phil can build 3 birdhouses in 5 days. Assuming he builds birdhouses at a constant rate, write the linear equation that represents the situation. Answer: Let y represent the total number of birdhouses Phil can build in x days. We can write \(\frac{y}{x}\) = \(\frac{3}{5}\) and y = \(\frac{3}{5}\) x.

Exercise 5. Explain your general strategy for comparing proportional relationships. Answer: When comparing proportional relationships, we look specifically at the rate of change for each situation. The relationship with the greater rate of change will end up producing more, painting a greater area, or walking faster when compared to the same amount of time with the other proportional relationship.

Eureka Math Grade 8 Module 4 Lesson 22 Problem Set Answer Key

Question 1. a. Train A can travel a distance of 500 miles in 8 hours. Assuming the train travels at a constant rate, write the linear equation that represents the situation. Answer: Let y represent the total number of miles Train A travels in x minutes. We can write \(\frac{y}{x}\) = \(\frac{500}{8}\) and y = \(\frac{125}{2}\) x.

Question 2. a. Natalie can paint 40 square feet in 9 minutes. Assuming she paints at a constant rate, write the linear equation that represents the situation. Answer: Let y represent the total square feet Natalie can paint in x minutes. We can write \(\frac{y}{x}\) = \(\frac{40}{9}\), and y = \(\frac{40}{9}\) x.

Question 3. a. Bianca can run 5 miles in 41 minutes. Assuming she runs at a constant rate, write the linear equation that represents the situation. Answer: Let y represent the total number of miles Bianca can run in x minutes. We can write \(\frac{y}{x}\) = \(\frac{5}{41}\), and y = \(\frac{5}{41}\) x.

Question 4. a. Geoff can mow an entire lawn of 450 square feet in 30 minutes. Assuming he mows at a constant rate, write the linear equation that represents the situation. Answer: Let y represent the total number of square feet Geoff can mow in x minutes. We can write \(\frac{y}{x}\) = \(\frac{450}{30}\), and y = 15x.

Question 5. a. Juan can walk to school, a distance of 0.75 mile, in 8 minutes. Assuming he walks at a constant rate, write the linear equation that represents the situation. Answer: Let y represent the total distance in miles that Juan can walk in x minutes. We can write \(\frac{y}{x}\) = \(\frac{0.75}{8}\), and y = \(\frac{3}{32}\) x.

Eureka Math Grade 8 Module 4 Lesson 22 Exit Ticket Answer Key

Question 1. Water flows out of Pipe A at a constant rate. Pipe A can fill 3 buckets of the same size in 14 minutes. Write a linear equation that represents the situation. Answer: Let y represent the total number of buckets that Pipe A can fill in x minutes. We can write \(\frac{y}{x}\) = \(\frac{3}{14}\) and y = \(\frac{3}{14}\) x.

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