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Texas Go Math Grade 8 Lesson 3.2 Answer Key Rate of Change and Slope
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 3.2 Answer Key Rate of Change and Slope.
Essential Question How do you find a rate of change or a slope?
Texas Go Math Grade 8 Lesson 3.2 Explore Activity Answer Key
Using Graphs to Find Rates of Change You can also use a graph to find rates of change.
Rate of Change and Slope Answer Key Go Math Grade 8 Question 2. Make a Conjecture Does a proportional relationship have a constant rate of change? Answer: Yes. The following equation holds: \(\frac{y}{x}\) = k Where k is the constant rate of change Yes
Question 3. Does it matter what interval you use when you find the rate of change of a proportional relationship? Explain. Answer: No. It does not matter what interval you use as long the order of points remains the same. When y is subtracted from y 2 , then x 1 should be subtracted from x 2 .
Texas Go Math Grade 8 Lesson 3.2 Guided Practice Answer Key
Tell whether the rates of change are constant or variable. (example 1)
Erica walks to her friend Philip’s house. The graph shows Erica’s distance from home over time. (Explore Activity)
Find the slope of each line. (Example 2)
Run = -2 – 0 = -2 Run is the difference in values represented by the x-axis
Essential Question Check-In
Question 9. If you know two points on a line, how can you find the rate of change of the variables being graphed? Answer: If the two given points are (x 1 , y 1 ) and (x 2 , y 2 ) we can find the slope slope = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) since the slope of a line is the ratio of the change in y-values for a segment of the graph to the corresponding change in x-values.
You can calculate the slope (See inside for more)
Texas Go Math Grade 8 Lesson 3.2 Independent Practice Answer Key
Question 10. Rectangle EFGH is graphed on a coordinate plane with vertices at E(-3, 5), F(6, 2), G(4, -4), and H(-5, -1).
a. Find the slopes of each side. Answer: We are given the vertices of the rectangle EFGH: E(-3, 5) F(6, 2) G(4, -4) H(-5, -1)
b. What do you notice about the slopes of opposite sides? Answer: The slopes of opposite sides are equal slope EF = slope GH = – \(\frac{1}{3}\) Slope FG = slope HE = 3
Question 12. Multistep A line passes through (6, 3), (8,4), and (n, -2). Find the value of n. Answer: Using the first two points: (x 1 , y 1 ) = (6, 3) and (x 2 , y 2 ) = (8, 4) find the slope of the line. Slope = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) = \(\frac{4-3}{8-6}\) = \(\frac{1}{2}\) Now use any of the first two points ant the last point to find the value of n by using the definition of a slope of the line: Slope = \(\frac{1}{2}\) = \(\frac{4-(-2)}{8-n}\) = \(\frac{6}{8-n}\) \(\frac{6}{12}\) = \(\frac{6}{8-n}\) Multiply the numerator and denominator of the left side by 6 12 = 8 – n n = -4
b. After how many minutes will the container be empty? Answer: No of minutes = = 25 \(\frac{5}{0.2}\) = 25 The number of minutes is determined by dividing the total volume of container by rate of water leakage. It will take $25$ minutes for the container to be empty.
Question 14. Critique Reasoning Billy found the slope of the line through the points (2, 5) and (-2, -5) using the equation \(\frac{2-(-2)}{5-(-5)}\) = \(\frac{2}{5}\). What mistake did he make? Answer: By definition, the slope is the change in y-values (rise) for a segment of the graph to the corresponding change in Slope = \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) Meanwhile, Billy wrote it as \(\frac{x_{-} 2-x_{-} 1}{y_{2}-y_{1}}\) So the real slope is \(\frac{5}{2}\) Billy got the reciprocal of the slope.
b. What do you notice about the slopes? Answer: The slopes of opposite sides are equal. slope AB = slope CD = – 1 slope BC = Slope DA = \(\frac{1}{2}\)
Texas Go Math Grade 8 Lesson 3.2 H.O.T. Focus On Higher Order Thinking Answer Key
Question 16. Communicate Mathematical Ideas Ben and Phoebe are finding the slope of a line. Ben chose two points on the line and used them to find the slope. Phoebe used two different points to find the slope. Did they get the same answer? Explain. Answer: Yes, they did. The slope of a line can be calculated using every two points on the line, since it is the same lane it has a unique (singular) slope
Yes, the slope is the same for every two points.
Lesson 3.2 Rate of Change and Slope Answer Key Question 17. Analyze Relationships Two lines pass through the origin. The lines have slopes that are opposites. Compare and contrast the lines. Answer: Since the slopes of the lines are opposites (if one line has a slope k the other has -k) it means they are equally steep, but since one has a positive slope it is slanted upwards from left to right and the other with the negative slope is slanted downwards.
One line is upward facing and the other is downward, but both are equally steep.
Question 18. Reason Abstractly What is the slope of the x-axis? Explain. Answer: The slope of a line is the ratio of the change in y-values for a segment of the graph to the corresponding change in x-values x-axis is a horizontal line that never changes its y-position, so the numerator of the ratio is zero Therefore, the slope of the x-axis is 0.
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Rate of Change and Slope Practice and Problem Solving: D Tell whether the rates of change are constant or variable. The first one is done for you. 1. calories per serving _____ 2. distance jumped _____ Servings 1 2 5 7 Jumps 2 4 7 10 Calories 150 300 750 1,050 Distance (ft) 12 24 35 55 Find the slope of each line.
32. The slope of the line that passes through (—2, Il) and (5, 6) is — Find the slope of the line that passes through each pair of points. Express as a fraction in simplest form. 102.3 - average rate of change = 100.5 The average rate of change in Lisa's temperature is 0.150th. 98.6-103.1 average rate of change = The average rate of change ...
Rate of Change and Slope Practice and Problem Solving: A/B Find the slope of each line. 1. slope ! _____ 2. slope ! _____ Solve. 3. Jasmine bought 7 yards of fabric. The total cost was $45.43. What was the average cost per yard of the fabric she bought? _____ 4. A train traveled 325 miles in 5 hours. What was the train's average rate
Rate of Change and Slope Practice and Problem Solving: D Tell whether the rates of change are constant or variable. The first one is done for you. 1. calories per serving _____ 2. distance jumped _____ Servings 1 2 5 7 Jumps 2 4 7 10 Calories 150 300 750 1,050 Distance (ft) 12 24 35 55 Find the slope of each line.
LESSON 3-2 90 60 30 Date Rate of Change and Slope Practice and Problem Solving: A/B Class 2. slope = Find the slope of each line. 1. slope = Solve. 3. Jasmine bought 7 yards of fabric. The total cost was $45.43. What was ... Explain your answer. Water in a Tank 01 23 Time (min) 7. A line passes through (l, 1), (—2, 4), and (6, n).
Practice and Problem Solving: D 1. constant 2. variable 3. 4. 1 5. 1 2 6. 2 5 7. 218 gal/h 8. 50 mi/h Reteach 1. increase 2. down 3. When the slope is positive, as the value of y increases, the value of x increases. 4. When the slope is positive, as you move from left to right, the line goes up. 5. Reading Strategies 1. (5, 4), (10, 8), (15, 12 ...
4. Find the slope of CD. 5. Study with Quizlet and memorize flashcards containing terms like 2. Find the slope of AB, 3. Find the slope of BC, 4. Find the slope of CD and more.
Problem-Solving Investigation: Use a Venn Diagram. Use a Venn diagram to solve each problem. PHONE SERVICE Of the 5,750 residents of Homer, Alaska, 2,330 pay for landline phone service and 4,180 pay for cell phone service. One thousand seven hundred fifty pay for both landline and cell phone service.
Lesson/Title Page 1-1 A Plan for Problem Solving .....1 1-2 Variables, Expressions, and Properties ... 5-5 Problem-Solving Investigation: Reasonable Answers .....42 5-6 Percent and ... Practice A Plan for Problem Solving Toppings Price 1 $12.99 2 $13.79 3 $14.59 4 $15.39
Rate of Change and Slope Practice and Problem Solving: D Tell whether the rates of change are constant or variable. The first one is done for you. 1. calories per serving _____ 2. distance jumped _____ Servings 1 2 5 7 Jumps 2 4 7 10 Calories 150 300 750 1,050 Distance (ft) 12 24 35 55 Find the slope of each line.
Our resource for Glencoe MATH Course 2, Volume 1 includes answers to chapter exercises, as well as detailed information to walk you through the process step by step. With Expert Solutions for thousands of practice problems, you can take the guesswork out of studying and move forward with confidence. Find step-by-step solutions and answers to ...
Lesson 3 Homework Practice Convert Unit Rates Convert each rate. Round to the nearest hundredth if necessary. ... 3. 17 cm/min = m/h 4. 815 gal/h ≈ qt/sec 5. 39 ft/min ≈ yd/s 6. 6,000 lb/day = T/wk 7. 110 mi/h = mi/day 8. 2 lb/wk ≈ oz/day 9. 90 ft/h ≈ mi/min 10. 44 mi/h ≈ yd/min 11. 22 lb/day ≈ oz/h 12. 720 pt/h ≈ qt/min
Solving Unit Rate Problems 6.RP.2, 6.RP.3.b LESSON 3 A rate is a comparison, or ratio, of two quantities with different units. For example, a store sells 3 T-shirts for $15. The comparison $15 to 3 T-shirts is a rate. This rate can also be written as $15 _____ 3 T-shirts. When a rate compares a quantity to one unit of another quantity, the rate ...
3, and the slope of g(x) is −3. Both y-intercepts are −2. The graphs are perpendicular and intersect at (0, −2). 3. Jing: $12.50, $0.50/year; Max: $10, $1/year; Sample answer: Jing starts at a higher wage, but gets a smaller raise each year. They both must work 6 years for Max to make more than Jing. Practice and Problem Solving: D 1. f ...
UNIT 2: Rates and Proportional Relationships MODULE 4 Rates and Proportionality LESSON 4-1 Practice and Problem Solving: A/B 1. 2 eggs per batch 2. 53 mph 3. $8/h 4. 14 points per game 5. $0.20/oz 6. 3 1 4 gal/h 7. 1 2 ft/min 8. Food A: 200 cal/serving; Food B: 375 cal/serving; Food A has fewer calories per serving. Practice and Problem Solving ...
By definition, the slope is the change in y-values (rise) for a segment of the graph to the corresponding change in. Slope = y2−y1 x2−x1. Meanwhile, Billy wrote it as x−2−x−1 y2−y1. So the real slope is 52. Billy got the reciprocal of the slope. Lesson 3.2 Rate of Change and Slope Reteach Answer Key Question 15.
Concept: for slope choose any point on graph say point P (a,b) …. LESSON Interpreting the Unit Rate as Slope 3-3 Practice and Problem Solving: AB Find the slope. Name the unit rate. 1 Benjamin Hiking 2. Marcy Hiking Tumehl 5 10 Distance (mi) 6 12 15 20 20 18 24 Distance (ml) 10 20 10 Time (h) Slope = Slope - Unit rate: Unit rate: Piyush ...
CCSS.MATH.CONTENT.6.RP.A.3. : "Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations." These worksheets can help students practice this Common Core State Standards skill.
The point of intersection of the x-axis and y-axis on a coordinate plane. Breaking down a composite number until all of the factors are prime. A ratio comparing two quantities with different kinds of units. A comparison of two quantities by division. The ratio of 2 to 3 can be stated as 2 out of 3, 2 to 3, 2:3, or 2/3.
Lesson 3 Problem-Solving Practice Probability of Compound Events 1. GASOLINE Craig stops at a gas station to fill his gas tank. He must choose between full-service or self-service and between regular, mid-grade, and premium gasoline. Draw a tree diagram showing the possible combinations of service and gasoline type. How many
Unit 7 Practice Problems - Answer Key. Problem 3 Here is a square and some regular octagons. Solution ... Lesson 3) Lin's puppy is gaining weight at a rate of 0.125 pounds per day. Describe the weight gain in days per pound. ... Problem 5 (from Unit 6, Lesson 8) Solve each equation. Solution 1. 2. 3. 2.1 4. 2.43 Problem 6
3. H IJ Q P O 4. EW SL H G MR Lesson 3 Skills Practice Similarity and Transformations yes; Sample answer: A rotation and a dilation with a scale factor of 2 maps EFG onto XYW. yes; Sample answer: A rotation and a dilation with a scale factor of 2 maps HIJ onto QOP. no; Sample answer: The ratios of the side lengths are not equal for all the ...
Answer to Solved Lesson 3 Homework Practice Convert Unit Rates Convert | Chegg.com. Skip to main content. Books. Rent/Buy; Read; ... Our expert help has broken down your problem into an easy-to-learn solution you can count on. ... Lesson 3 Homework Practice Convert Unit Rates Convert each rate. Round to the nearest hundredth if necessary. ft/h ...