{"id":85779,"date":"2022-05-30T14:12:51","date_gmt":"2022-05-30T08:42:51","guid":{"rendered":"https:\/\/ccssanswers.com\/?p=85779"},"modified":"2022-05-10T14:19:44","modified_gmt":"2022-05-10T08:49:44","slug":"eureka-math-grade-8-module-4-lesson-15","status":"publish","type":"post","link":"https:\/\/ccssanswers.com\/eureka-math-grade-8-module-4-lesson-15\/","title":{"rendered":"Eureka Math Grade 8 Module 4 Lesson 15 Answer Key"},"content":{"rendered":"

Engage NY Eureka Math 8th Grade Module 4 Lesson 15 Answer Key<\/h2>\n

Eureka Math Grade 8 Module 4 Lesson 15 Opening Exercise Answer Key<\/h3>\n

\"Eureka<\/p>\n

a. Which graph is steeper?
\nAnswer:
\nIt looks like Graph B is steeper.<\/p>\n

b. Write directions that explain how to move from one point on the graph to the other for both Graph A and Graph B.
\nAnswer:
\nFor Graph A, move 2 units up and 3 units right. For Graph B, move 4 units up and 3 units right.<\/p>\n

c. Write the directions from part (b) as ratios, and then compare the ratios. How does this relate to which graph was steeper in part (a)?
\nAnswer:
\n\\(\\frac{2}{3}\\)<\\(\\frac{4}{3}\\).<\/p>\n

Pair 1:
\n\"Eureka<\/p>\n

a. Which graph is steeper?
\nAnswer:
\nIt looks like Graph A is steeper.<\/p>\n

b. Write directions that explain how to move from one point on the graph to the other for both Graph A and Graph B.
\nAnswer:
\nFor Graph A, move 4 units up and 5 units right. For Graph B, move 1 unit up and 12 units right.<\/p>\n

c. Write the directions from part (b) as ratios, and then compare the ratios. How does this relate to which graph was steeper in part (a)?
\nAnswer:
\n\\(\\frac{4}{5}\\)>\\(\\frac{1}{12}\\). Graph A was steeper and had the greater ratio.<\/p>\n

Pair 2:
\n\"Eureka<\/p>\n

a. Which graph is steeper?
\nAnswer:
\nIt looks like Graph A is steeper.<\/p>\n

b. Write directions that explain how to move from one point on the graph to the other for both Graph A and Graph B.
\nAnswer:
\nFor Graph A, move 7 units up and 1 unit right. For Graph B, move 3 units up and 6 units right.<\/p>\n

c. Write the directions from part (b) as ratios, and then compare the ratios. How does this relate to which graph was steeper in part (a)?
\nAnswer:
\n\\(\\frac{7}{1}\\)>\\(\\frac{3}{6}\\). Graph A was steeper and had the greater ratio.<\/p>\n

Pair 3:
\n\"Eureka<\/p>\n

a. Which graph is steeper?
\nAnswer:
\nIt looks like Graph B is steeper.<\/p>\n

b. Write directions that explain how to move from one point on the graph to the other for both Graph A and Graph B.
\nAnswer:
\nFor Graph A, move 1 unit up and 5 units right. For Graph B, move 4 units up and 1 unit right.<\/p>\n

c. Write the directions from part (b) as ratios, and then compare the ratios. How does this relate to which graph was steeper in part (a)?
\n\\(\\frac{1}{5}\\)<\\(\\frac{4}{1}\\). Graph B was steeper and had the greater ratio.<\/p>\n

Pair 4:
\n\"Eureka<\/p>\n

a. Which graph is steeper?
\nAnswer:
\nThey look about the same steepness.<\/p>\n

b. Write directions that explain how to move from one point on the graph to the other for both Graph A and Graph B.
\nAnswer:
\nFor Graph A, move 4 units up and 4 units right. For Graph B, move 3 units up and 3 units right.<\/p>\n

c. Write the directions from part (b) as ratios, and then compare the ratios. How does this relate to which graph was steeper in part (a)?
\nAnswer:
\n\\(\\frac{4}{4}\\)=\\(\\frac{3}{3}\\). The graphs have equal ratios, which may explain why they look like the same steepness.<\/p>\n

Eureka Math Grade 8 Module 4 Lesson 15 Exercise Answer Key<\/h3>\n

Use your transparency to find the slope of each line if needed.<\/p>\n

Exercise 1.
\nWhat is the slope of this non-vertical line?
\n\"Eureka
\nAnswer:
\nThe slope of this line is 4, m=4.<\/p>\n

Exercise 2.
\nWhat is the slope of this non-vertical line?
\n\"Eureka
\nAnswer:
\nThe slope of this line is 3, m=3.<\/p>\n

Exercise 3.
\nWhich of the lines in Exercises 1 and 2 is steeper? Compare the slopes of each of the lines. Is there a relationship between steepness and slope?
\nAnswer:
\nThe graph in Exercise 1 seems steeper. The slopes are 4 and 3. It seems like the greater the slope, the steeper the line.<\/p>\n

Exercise 4.
\nWhat is the slope of this non-vertical line?
\n\"Eureka
\nAnswer:
\nThe slope of this line is -1, m=-1.<\/p>\n

Exercise 5.
\nWhat is the slope of this non-vertical line?
\n\"Eureka
\nAnswer:
\nThe slope of this line is -4, m=-4.<\/p>\n

Exercise 6.
\nWhat is the slope of this non-vertical line?
\n\"Eureka
\nAnswer:
\nThe slope of this line is 0, m=0.<\/p>\n

Eureka Math Grade 8 Module 4 Lesson 15 Problem Set Answer Key<\/h3>\n

Students practice identifying lines as having positive or negative slope. Students interpret the unit rate of a graph as the slope of the graph.<\/p>\n

Question 1.
\nDoes the graph of the line shown below have a positive or negative slope? Explain.
\n\"Eureka
\nAnswer:
\nThe graph of this line has a negative slope. First of all, it is left-to-right declining, which is an indication of negative slope. Also, if we were to mark a point P and a point Q one unit to the right of P and then draw a line parallel to the y-axis through Q, then the intersection of the two lines would be below Q, making the number that represents slope negative.<\/p>\n

Question 2.
\nDoes the graph of the line shown below have a positive or negative slope? Explain.
\n\"Eureka
\nAnswer;
\nThe graph of this line has a positive slope. First of all, it is left-to-right inclining, which is an indication of positive slope. Also, if we were to mark a point P and a point Q one unit to the right of P and then draw a line parallel to the y-axis through Q, then the intersection of the two lines would be above Q, making the number that represents slope positive.<\/p>\n

Question 3.
\nWhat is the slope of this non-vertical line? Use your transparency if needed.
\n\"Eureka
\nAnswer:
\nThe slope of this line is 1, m=1.<\/p>\n

Question 4.
\nWhat is the slope of this non-vertical line? Use your transparency if needed.
\n\"Eureka
\nAnswer:
\nThe slope of this line is –\\(\\frac{3}{2}\\), m=-\\(\\frac{3}{2}\\).<\/p>\n

Question 5.
\nWhat is the slope of this non-vertical line? Use your transparency if needed.
\n\"Eureka
\nAnswer:
\nThe slope of this line is \\(\\frac{5}{2}\\), m=\\(\\frac{5}{2}\\).<\/p>\n

Question 6.
\nWhat is the slope of this non-vertical line? Use your transparency if needed.
\n\"Eureka
\nAnswer:
\nThe slope of this line is 16, m=16.<\/p>\n

Question 7.
\nWhat is the slope of this non-vertical line? Use your transparency if needed.
\n\"Eureka
\nAnswer:
\nThe slope of this line is -10, m=-10.<\/p>\n

Question 8.
\nWhat is the slope of this non-vertical line? Use your transparency if needed.
\n\"Eureka
\nAnswer:
\nThe slope of this line is -5, m=-5.<\/p>\n

Question 9.
\nWhat is the slope of this non-vertical line? Use your transparency if needed.
\n\"Eureka
\nAnswer:
\nThe slope of this line is 2, m=2.<\/p>\n

Question 10.
\nWhat is the slope of this non-vertical line? Use your transparency if needed.
\n\"Eureka
\nAnswer:
\nThe slope of this line is -2, m=-2.<\/p>\n

Question 11.
\nWhat is the slope of this non-vertical line? Use your transparency if needed.
\n\"Eureka
\nAnswer:
\nThe slope of this line is 2, m=2.<\/p>\n

Question 12.
\nWhat is the slope of this non-vertical line? Use your transparency if needed.
\n\"Eureka
\nAnswer:
\nThe slope of this line is 5, m=5.<\/p>\n

Question 13.
\nWhat is the slope of this non-vertical line? Use your transparency if needed.
\n\"Eureka
\nAnswer:
\nThe slope of this line is \\(\\frac{3}{2}\\), m=\\(\\frac{3}{2}\\).<\/p>\n

Question 14
\nWhat is the slope of this non-vertical line? Use your transparency if needed.
\n\"Eureka
\nAnswer:
\nThe slope of this line is 0, m=0.<\/p>\n

In Lesson 11, you did the work below involving constant rate problems. Use the table and the graphs provided to answer the questions that follow.<\/p>\n

Question 15.
\nSuppose the volume of water that comes out in three minutes is 10.5 gallons.
\n\"Eureka<\/p>\n

a. How many gallons of water flow out of the faucet per minute? In other words, what is the unit rate of water flow?
\nAnswer:
\nThe unit rate of water flow is 3.5 gallons per minute.<\/p>\n

b. Assume that the graph of the situation is a line, as shown in the graph. What is the slope of the line?
\nAnswer:
\nThe slope of the line is 3.5, m=3.5.<\/p>\n

Question 16.
\nEmily paints at a constant rate. She can paint 32 square feet in five minutes.
\n\"Eureka<\/p>\n

a. How many square feet can Emily paint in one minute? In other words, what is her unit rate of painting?
\nAnswer:
\nThe unit rate at which Emily paints is 6.4 square feet per minute.<\/p>\n

b. Assume that the graph of the situation is a line, as shown in the graph. What is the slope of the line?
\nAnswer:
\nThe slope of the line is 6.4, m=6.4.<\/p>\n

Question 17.
\nA copy machine makes copies at a constant rate. The machine can make 80 copies in 2 1\/2 minutes.
\n\"Eureka
\n\"Eureka
\na. How many copies can the machine make each minute? In other words, what is the unit rate of the copy machine?
\nAnswer:
\nThe unit rate of the copy machine is 32 copies per minute.<\/p>\n

b. Assume that the graph of the situation is a line, as shown in the graph. What is the slope of the line?
\nAnswer:
\nThe slope of the line is 32, m=32.<\/p>\n

Eureka Math Grade 8 Module 4 Lesson 15 Exit Ticket Answer Key<\/h3>\n

Question 1.
\nWhat is the slope of this non-vertical line? Use your transparency if needed.
\n\"Engage
\nAnswer:
\nThe slope of the line is 3, m=3.<\/p>\n

Question 2.
\nWhat is the slope of this non-vertical line? Use your transparency if needed.
\n\"Engage
\nAnswer:
\nThe slope of the line is -0.6, which is equal to –\\(\\frac{3}{5}\\), m=-\\(\\frac{3}{5}\\).<\/p>\n","protected":false},"excerpt":{"rendered":"

Engage NY Eureka Math 8th Grade Module 4 Lesson 15 Answer Key Eureka Math Grade 8 Module 4 Lesson 15 Opening Exercise Answer Key a. Which graph is steeper? Answer: It looks like Graph B is steeper. b. Write directions that explain how to move from one point on the graph to the other for … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/85779"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=85779"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/85779\/revisions"}],"predecessor-version":[{"id":137157,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/85779\/revisions\/137157"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=85779"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=85779"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=85779"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}