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## Go Math! 6 Common Core Edition, Grade: 6 Publisher: Houghton Mifflin Harcourt

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## Texas Go Math Grade 8 Lesson 6.3 Answer Key Comparing Functions

Refer to our Texas Go Math Grade 8 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 8 Lesson 6.3 Answer Key Comparing Functions.

Essential Question How can you use tables, graphs, and equations to compare functions?

Texas Go Math Grade 8 Lesson 6.3 Explore Activity Answer Key

Explore Activity 1

A. Find Morgan’s unit rate.

B. Find Brian’s unit rate.

C. Which student types more correct words per minute?

Lesson 6.3 Comparing Functions Answer Key Go Math 8th Grade Question 2. Katie types 17 correct words per minute. Explain how a graph of Katie’s test results would compare to Morgan’s and Brian’s. Answer: Katie types 17 correct words per minute; Brian types 20 correct words per minute and Morgan types 15 correct words per minute. Therefore, the graph of Katie’s test results will be a straight line that passes through the origin (0, 0). The value of its slope is greater than the slope of Morgan’s graph of test results and smaller than the slope of Brian’s graph of test results. So, the graph will be a straight line that lies between the line of Morgan and Brian.

A. Write an equation in slope-intercept form for Store A’s layaway plan. Let x represent the number of weeks and y represent the balance owed.

B. Write an equation in slope-intercept form for Store B’s layaway plan. Let x represent the number of weeks and y represent the balance owed.

C. Sketch a graph of the plan at Store B on the same grid as Store A.

D. How can you use the graphs to tell which plan requires the greater down payment? How can you use the equations?

E. How can you Use the graphs to tell which plan requires the greater weekly payment? How can you use the equations?

F. Which plan allows Jamal to pay for the game system faster? Explain.

Texas Go Math Grade 8 Lesson 6.3 Guided Practice Answer Key

Doctors have two methods of calculating maximum heart rate. With the first method, the maximum heart rate,y, in beats per minute is y = 220 – x, where x is the person’s age. The maximum heart rate with the second method is shown in the table. (Example 1)

Question 1. Which method gives the greater maximum heart rate for a 70-year-old? Answer: y = 220 – x First method y = 220 – 70 = 150 Substitute x = 70 yrs slope = \(\frac{187-194}{30-20}\) = \(\frac{-7}{10}\) = -0.7 Writing the equation for the second method. Find the slope using given points by slope (m) = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) where (x 2 , y 2 ) = (30, 187) and (x 1 , y 1 ) = (20, 194) 194 = -0.7(20) + b Substituting the value of slope (m) and (x, y) in the slope-intercept form to find y-intercept (b): y = mx + b 194 = -14 + b b = 194 + 14 = 208

y = 208 – 0.7x Substituting the value of slope (m) and y-intercept (b) in slope-intercept form: y = mx + b y = 208 – 0.7(70) = 159 Substitute x = 70 yrs The second method gives the greater maximum heart rate for a 70-year-old methods

Compare the maximum heart rate for the two methods 150 < 159

Question 2. Are heart rate and age proportional or nonproportional for each method? Answer: For method 1, the relationship is non-proportional. Comparing with the general linear form of an equation: y = mx + b. For method 2, the relationship is non-proportional. Since b ≠ 0, the relationship is not proportional.

Aisha runs a tutoring business. With Plan 1, students may choose to pay $15 per hour. With Plan 2, they may follow the plan shown on the graph. (Explore Activity 1 and 2)

Question 3. Describe the plan shown on the graph. Answer: We choose two points on the graph to find the slope. We substitute (0, 40) for (x 1 , y 1 ) and (4, 60) for (x 2 , y 2 ). m = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) = \(\frac{60-40}{4-0}\) = \(\frac{20}{4}\) = 5 We read the y-intercept from the graph, which is 40. b = 40 We use the slope and y-intercept values that we found to write an equation in slope-intercept form. y = mx + b y = 5x + 40 This means that Plan 2 has an initial cost of $40 and a rate of $5 per hour

8th Grade Comparing Functions Answer Key Lesson 6.3 Question 5. What does the intersection of the two graphs mean? Answer: The intersection of the two graphs represents the number of hours for which both plans will cost the same.

Question 6. Which plan is cheaper for 10 hours of tutoring? Answer: Knowing that with Plan 1 student pays 15 dollars per hour, we can calculate the cost of 10 hours of tutoring. Variable y is the cost and variable æ is the number of hours. Therefore: y 1 = 15x y 1 = 15 . 10 y 1 =150

To calculate the cost of Plan 2, we will use the following formula: y 2 = 5x + 40, where variable y is the cost and variable x is the number of hours. Therefore: y 2 = 5 . 10 + 40 y 2 = 90 Hence, we can conclude that Plan 2 is cheaper for 10 hours of tutoring.

Question 7. Are cost and time proportional or nonproportional for each plan? Answer: The cost and time are proportional for Plan 1 Compared with the general linear form of equation: y = mx + b. Since b = 0, the relationship is proportional.

The cost and time are not proportional for Plan 2 Compared with the general linear form of equation: y = mx + b. Since b ≠ 0, the relationship is not proportional.

Essential Question Check-In

Go Math Grade 8 Lesson 6.3 Answer Key Question 8. When using tables, graphs, and equations to compare functions, why do you find the equations for tables and graphs? Answer: The tables and graphs represent a part of the solution of the function By writing the equation, any value can be substituted to evaluate the function and compare it with the equations.

Texas Go Math Grade 8 Lesson 6.3 Independent Practice Answer Key

Question 9. Which scooter uses fewer gallons of gas when 1350 miles are driven? Answer: Looking at the given table for scooter A, we can conclude that scooter uses 2 gallons for every 150 miles. Therefore, we can write the equation where variable y represents used gallons of gas and variable x represents driven miles. y a = \(\frac{2 x}{150}\) y a = \(\frac{x}{75}\) Considering the fact that we are testing the consumption of gas for 1350 driven miles, we can use the equation for y a and insert x = 1350 as follows: y a = \(\frac{1350}{75}\) y a = 18 Given graph represents driven miles and gas used for scooter B. We will find value of driven miles for gas consumption of 1 gallon by drawing a horizontal line on the value of 1 gallon and looking for an intersection with the function. Lines intersect on x = 90, meaning that scooter B uses 1 gallon of gas for 90 driven miles. Therefore: y b = \(\frac{x}{90}\), where y b is the consumption of gas and variable x represents driven miles.

Using the equation obtained in the previous step, we can calculate gas consumption for 1350 driven miles. y b = \(\frac{1350}{90}\) y b = 15 Hence, we can conclude that scooter B uses fewer gallons of gas when driving 1350 miles.

Lesson 6.3 Answer Key 8th Grade Comparing Functions Question 10. Are gas used and miles proportional or nonproportional for each scooter? Answer: The gas used and miles are proportional for both scooters.

Comparing with the general linear form of an equation: y = mx + b. Since b = 0, the relationship is proportional.

Question 11. Which plan is cheaper for under 200 texts? ______ Answer: y = 0.10x + 5 Plan 1 y = 0.10(199) + 5 = $24.90 Substitute x = 199 slope = \(\frac{25-20}{200-100}\) = \(\frac{5}{100}\) = 0.05 Writing the equation for plan 2. Find the slope using given points by Slope (m) = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) where (x 2 , y 2 ) = (200, 25) (x 1 , y 1 ) = (100, 20) 20 = 0.05(100) + b Substituting the value of slope (m) and (x, y) in the slope-intercept form to find y-intercept (b): 20 = 5 + b y = mx + b b = 20 – 5 = 15 y = 0.05x + 15 Substituting the value of slope (m) and y-intercept (b) in slope-intercept form: y = mx + b y = 0.05(199) + 15 = $24.95 Substitute x = 199

Plan 1 is cheaper Compare the cost for two plans for text < 200 $24.90 < $24.95

Question 12. The graph of the first plan does not pass through the origin. What does this indicate? Answer: y = 0.10x + 5 Plan 1 The graph that does not pass through the origin indicates that there is a base price of $\$5$ for the plan.

Go Math 8th Grade Lesson 6.3 Comparing Functions Question 13. Brianna wants to buy a digital camera for a photography class. One store offers the camera for $50 down and a payment plan of $20 per month. The payment plan for a second store is described by y = 15x + 80, where y is the total cost in dollars and x is the number of months. Which camera is cheaper when the camera is paid off in 12 months? Explain. Answer: For us to determine which camera is cheaper when the camera is paid off in 12 months, let us determine the total cost of the digital camera offered by the two stores.

The first store offers the camera for $50 down and a payment of $20 per month. By applying the slope-intercept form y = mx + b. Let y be the total cost of the camera for the first store x be the number of months the camera needs to be paid off m be the payment every month b be the down payment

Substituting the values of m = 20, b = 50, and x = 12, the total cost of the camera offered by the first store is \begin{aligned} y&=mx+b\ y&=20(12)+50\ y&=240+50\ y&=290 \end{aligned}

Thus, the total cost of the camera offered by the first store is $290

The payment plan for the second store is described by y = 15x + 80 where y is the total. cost of the camera in dollars and x is the number of months

Thus, the total cost of the camera offered by the second store is $260

Now, let us compare the total costs of the camera offered by the two stores. The total cost of the camera offered by the first store is $290 while the second store camera’s total cost is $260. Since $260 is less than $290, then we can conclude that **the camera of the second store is cheaper than the camera of the first store**.

Texas Go Math Grade 8 Lesson 6.3 H.O.T. Focus On Higher Order Thinking Answer Key

Question 15. Draw Conclusions Gym A charges $60 a month plus $5 per visit. The monthly cost at Gym B is represented by y = 5x + 40, where x is the number of visits per month. What conclusion can you draw about the monthly costs of gyms? Answer: Since the rate per visit is the same, the monthly cost of Gym A is always more than Gym B

Comparing Functions Worksheet 8th Grade Answers Question 16. Justify Reasoning Why will the value of y for the function y = 5x + 1 always be greater than that for the function y = 4x + 2 when x > 1? Answer: y 1 = 5x + 1 and y 2 = 4x + 2 Subtracting y 2 from y 1 we get y 1 – y 2 = 5x + 1 – (4x + 2) y 1 – y 2 = x – 1 For x ≥ 1 we get x – 1 ≥ 0 So, y 1 – y 2 ≥ 0 or y 1 ≥ y 2 Hence proved.

Question 17. Analyze Relationships The equations of two functions are y = -21x + 9 and y = -24x + 8. Which function is changing more quickly? Explain. Answer: To determine among the given equations of functions changing more quickly, we have to determine the absolute value of slope of the equations and then compare them. If the absolute value of the slope of one equation is greater than the slope of the other, then this equation changing more quickly than the other.

Determining the slopes of the two equations below. y = -21x + 9 y = -24x + 8 Since, the two equations are already in the form of y = mx + b, where m is the slope, it is easier to determine their slope and these are | Equation | Slope | |–|–| |y = -21x + 9 | -21| |y = -24x + 81 -24| Now, Let us get the absolute values of the two slopes. |- 21| = 21 |-24| = 24

The absolute value of the slope of the equation y = -21x + 9 is 21 while of the equation y = -24x + 8 is 24. Since 24 is greater than 21, then the equation y = -24x + 8 changes more quickly than the equation y = -21x + 9. See the explanation

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## Eureka Math Grade 3 Module 6 Lesson 7 Answer Key

Engage ny eureka math 3rd grade module 6 lesson 7 answer key, eureka math grade 3 module 6 lesson 7 pattern sheet answer key.

## Eureka Math Grade 3 Module 6 Lesson 7 Problem Set Answer Key

Question 1. Mrs. Weisse’s class grows beans for a science experiment. The students measure the heights of their bean plants to the nearest \(\frac{1}{4}\) inch and record the measurements as shown below.

## Eureka Math Grade 3 Module 6 Lesson 7 Exit Ticket Answer Key

Question 1. Scientists measure the growth of mice in inches. The scientists measure the length of the mice to the nearest \(\frac{1}{4}\) inch and record the measurements as shown below.

## Eureka Math Grade 3 Module 6 Lesson 7 Homework Answer Key

Question 1. Mrs. Felter’s students build a model of their school’s neighborhood out of blocks. The students measure the heights of the buildings to the nearest \(\frac{1}{4}\) inch and record the measurements as shown below.

## Eureka Math Grade 3 Module 6 Answer Key

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Answer: Eureka Math Grade 3 Module 6 Lesson 8 Problem Set Answer Key Question 1. Delilah stops under a silver maple tree and collects leaves. At home, she measures the widths of the leaves to the nearest inch and records the measurements as shown below. a. Use the data to create a line plot below. b.

EngageNY/Eureka Math Grade 3 Module 6 Lesson 8For more videos, please visit http://bit.ly/eurekapusdPLEASE leave a message if a video has a technical difficu...

lesson 8 homework module 6 grade 3 - YouTube You can find the source for the homework pages at the link below. I used the "full module"...

Example 1. Ordering Rational Numbers from Least to Greatest Sam has $10.00 in the bank. He owes his friend Hank $2.25. He owes his sister $1.75. Consider the three rational numbers related to this story of Sam's money. Write and order them from least to greatest. Answer: - 2.25, - 1.75, 10.00 Example 2.

Illustrative Mathematics Grade 8 Open Up Resources OURUnit 3 Lesson 6More resources available at: mathhelp.cusd.com

Eureka Math Grade 3 Module 6 Lesson 8 Answer Key; Eureka Math Grade 3 Module 6 Lesson 9 Answer Key; Eureka Math Grade 3 Module 6 End of Module Assessment Answer Key. Summary. Hope the knowledge shared has shed some light on you regarding the Eureka Math Grade 3 Module 6 Answer Key. For more information feel free to reach us via the comment ...

Lesson 8 Homework Practice Volume and Surface Area of Composite Figures Find the volume of each composite figure. 1. 2 ft 1.5 ft 4 ft 2 ft 2. 6 cm 6 cm 6 cm 5 cm 5 cm 0.5 cm 0.5 cm 0.5 cm 3. ... 6. 8 cm 3.6 cm 3.6 cm 2 cm 3 cm 2 cm 6 cm area of base7. 3.6 ft 3.6 ft 2 ft 3.6 ft 4 ft 5.6 ft2 1 in. 30 in. 20 in. 984 in3

Chapter 1: Rational Numbers Page 3: Are You Ready? Section 1.1: Rational Numbers Section 1.2: Multiplying Rational Numbers Section 1.3: Dividing Rational Numbers Section 1.4: Adding and Subtracting with Unlike Denominators Section 1.5: Solving Equations with Rational Numbers Section 1.6: Solving Two-Step Equations Page 40: Study Guide: Review

Answer Key GRADE 3 • MODULE 3 Multiplication and Division with Units of 0, 1, 6─9, and Multiples of 10 Module 3: Date: Multiplication and Division with Units of 0, 1, 6─9, and Multiples of 10 8/1/14 2014 Common Core, Inc. Some rights reserved. commoncore.org This work is licensed under a

Chapter 13: Variability and Data Distributions. Go Math! 6 Common Core Edition grade 6 workbook & answers help online. Grade: 6, Title: Go Math! 6 Common Core Edition, Publisher: Houghton Mifflin Harcourt, ISBN: 547587783.

Free math problem solver answers your algebra homework questions with step-by-step explanations.

Chapter 11: Congruence, Similarity, and Transformations. Section 11.1: Angle and Line Relationships. Section 11.2: Triangles. Find step-by-step solutions and answers to Glencoe Math Accelerated - 9780076637980, as well as thousands of textbooks so you can move forward with confidence.

The first one is done for you. a. 2 threes: 2 × 3 = 6 b. 3 twos: _________________ c. 3 fours: ________________ d. 4 threes: ________________ e. 3 sevens: ________________ f. 7 threes: ________________ g. 3 nines: _________________ h. 9 threes: ________________ i. 10 threes: _______________ b. 3 twos : 3 x 2 = 6, Explanation:

Lesson: 6 Count and Write to 8. Lesson 3.6 Count and Write to 8 - Page(149-154) Count and Write to 8 Homework & Practice 3.6 - Page(153-154) Lesson: 7 Model and Count 9. Lesson 3.7 Model and Count 9 - Page(155-160) Model and Count 9 Homework & Practice 3.7 - Page(159-160) Lesson: 8 Count and Write to 9

The source for the homework pages is the link below. Click on the "full module" PDF:https://www.engageny.org/resource/grade-3-mathematics-module-3

MATH Share and Show Identify the quadrant where the point is located. To graph the point, first move to the right from the origin, 2. 6. Quadrant: (1, Quadrant: Then move down Quadrant: Quadrant: 4. Quadrant: 5. Quadrant: The two points are reflections Of each other across the x- or y-axis. Identify the axis.

Draw a picture of the birds. Answer: 4 + 2 + 4 = 10. Beth sees = 10 birds. Final Words: Learn the basics like addition, subtraction from the primary level itself. Refer to Go Math Grade 1 Answer Key Chapter 3 Addition Strategies to score good marks in the exams. Download the free pdf of HMH Go Math 1st Grade Answer Key Chapter 3 from this page.

More about Constant SpeedPractice Problems - IM 6-8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyr...

Explanation: A. Drawn a square with 10 equal columns as shown above, The decimal value does each column represent is 0.1, B. Using a color pencil, shade columns on the grid to represent the distance to Charlene's school, The distance to the school is 0.8 mile, So columns shaded are 8,

A Multiply or Divide by 6 Question 1. 2 × 6 = Answer: 12 By multiplying 2 with 6 we get 12 Question 2. 3 × 6 = Answer: 18 By multiplying 3 with 6 we get 18 Question 3. 4 × 6 = Answer: 24 By multiplying 4 with 6 we get 24 Question 4. 5 × 6 = Answer: 30 By multiplying 5 with 6 we get 30 Question 5. 1 × 6 = Answer: 6 By multiplying 1 with 6 we get 6

y = mx + b. y = 5x + 40. This means that. Plan 2 has an initial cost of $40 and a rate of $5 per hour. Question 4. Sketch a graph of Plan 1 on the same grid as Plan 2. Answer: Plan 1 is represented by red and Plan 2 is represented by blue. 8th Grade Comparing Functions Answer Key Lesson 6.3 Question 5.

f. Savannah was absent the day the class measured the heights of their bean plants. When she returns, her plant measures 2 2 4 inches tall. Can Savannah plot the height of her bean plant on the class line plot? Why or why not? Answer: a. Title: Heights of Bean Plants (in Inches) Label: Bean Plants X = 1 bean plant