Spectrum Math Grade 8 Chapter 3 Lesson 1 Answer Key Understanding Slope

Students can use the Spectrum Math Grade 8 Answer Key Chapter 3 Lesson 3.1 Understanding SlopeĀ as a quick guide to resolve any of their doubts.

Spectrum Math Grade 8 Chapter 3 Lesson 3.1 Understanding Slope Answers Key

The slope of a line on a coordinate grid can be found by determining the rate of change.

Michael keeps track of the number of yards Fe mows for 5 days.
Spectrum Math Grade 8 Chapter 3 Lesson 1 Answer Key Understanding Slope 14
Find the slope, or rate of change, by dividing the rate of change for the dependent variable (amount earned) by the rate of change for the independent variable (number of lawns).
Spectrum Math Grade 8 Chapter 3 Lesson 1 Answer Key Understanding Slope 15
The rate of change, or slope, in this situation Ā”s 20 and is constant.

Find the slope, or rate of change for each situation. Be sure to show your work.

Question 1.
Students are buying tickets for the fall dance. The student council keeps track of how many tickets they sell in one week.
Spectrum Math Grade 8 Chapter 3 Lesson 1 Answer Key Understanding Slope 16
The rate The rate of change, or slope, for this situation is ____.
Answer:Ā  The rate The rate of change, or slope, for this situation is 5
The slope of a line on a coordinate grid can be found by determining the rate of change.
To find rate of change, divide the rate of change for the dependent variable by the rate of change for the independent variable.
\(\frac{Change in amount earned}{Change in no. of tickets sold}\) = \(\frac{75-50}{15-10}\) = \(\frac{25}{5}\) = 5
\(\frac{Change in amount earned}{Change in no. of tickets sold}\) = \(\frac{115-75}{23-15}\) = \(\frac{40}{8}\) = 5
The rate of change, or slope, in this situation is 5 and is constant.

Question 2.
Jean planted a sunflower. She decided to measure how much it grew each week.
Spectrum Math Grade 8 Chapter 3 Lesson 1 Answer Key Understanding Slope 17
The rate of change, or slope, for this situation is _____
Answer: The rate of change, or slope, for this situation is 4.2
The slope of a line on a coordinate grid can be found by determining the rate of change.
To find rate of change, divide the rate of change for the dependent variable by the rate of change for the independent variable.
\(\frac{Change in height}{Change in time}\) = \(\frac{20.4-16.2}{2-1}\) = \(\frac{4.2}{1}\) =4.2
\(\frac{Change in height}{Change in time}\) = \(\frac{24.6-20.4}{3-2}\) = \(\frac{4.2}{1}\) =4.2
The rate of change, or slope, in this situation is 4.2 and is constant.

Sometimes a rate of change is variable, or changes as data is collected.

Samantha kicks a ball and records a video o the ballā€™s path so she can observe its path.
Spectrum Math Grade 8 Chapter 3 Lesson 1 Answer Key Understanding Slope 18
Find the slope, or rate of change, by dividing the rate of change for dependent by the rate of change for the independent variable (height).
Spectrum Math Grade 8 Chapter 3 Lesson 1 Answer Key Understanding Slope 19
The rate of change, or slope, in this situation is variable because it collection point to another.

Determine if each slope, or rate of change, is constant or variable. Show your work.

Question 1.
Eric walks to his friendā€™s house.
Spectrum Math Grade 8 Chapter 3 Lesson 1 Answer Key Understanding Slope 3
The rate of change for this situation is ____
Answer: The rate of change for this situation is constant
The slope of a line on a coordinate grid can be found by determining the rate of change.
To find rate of change, divide the rate of change for the dependent variable by the rate of change for the independent variable.
\(\frac{Change in time}{Change in distance travelled}\) = \(\frac{10-5}{0.5-0.25}\) = \(\frac{5}{0.25}\) =20
\(\frac{Change in time}{Change in distance travelled}\) = \(\frac{15-10}{0.75-0.5}\) = \(\frac{5}{0.25}\) =20
The rate of change, or slope, in this situation is 20 and is constant.

Question 2.
Cindy went for a bike ride through town.
Spectrum Math Grade 8 Chapter 3 Lesson 1 Answer Key Understanding Slope 4
The rate of change for this situation is ____
Answer: The rate of change for this situation is variable.
The slope of a line on a coordinate grid can be found by determining the rate of change.
To find rate of change, divide the rate of change for the dependent variable by the rate of change for the independent variable.
\(\frac{Change in time}{Change in distance travelled}\) = \(\frac{10-5}{1.5-1.0}\) = \(\frac{5}{0.5}\) =10
\(\frac{Change in time}{Change in distance travelled}\) = \(\frac{15-10}{2.3-1.5}\) = \(\frac{5}{0.8}\) =6.25
The rate of change for this situation is variable.

Determine if each slope, or rate of change, is constant or variable. Show your work.

Question 1.
Johnson is ordering t-shirts for his school. The more he orders, the lower the cost per shirt is.
Spectrum Math Grade 8 Chapter 3 Lesson 1 Answer Key Understanding Slope 5
The rate of change for this situation is ____
Answer: The rate of change for this situation is variable.
The slope of a line on a coordinate grid can be found by determining the rate of change.
To find rate of change, divide the rate of change for the dependent variable by the rate of change for the independent variable.
\(\frac{Change in no. of t-shirts}{Change in total cost}\) = \(\frac{200-100}{900-500}\) = \(\frac{100}{400}\) =0.25
\(\frac{Change in no. of t-shirts}{Change in total cost}\) = \(\frac{300-200}{1200-900}\) = \(\frac{100}{300}\) =0.33
The rate of change for this situation is variable.

Question 2.
Bike rental costs $10 per hour.
Spectrum Math Grade 8 Chapter 3 Lesson 1 Answer Key Understanding Slope 6
The rate of change for this situation is ____
Answer: The rate of change for this situation is constant.
The slope of a line on a coordinate grid can be found by determining the rate of change.
To find rate of change, divide the rate of change for the dependent variable by the rate of change for the independent variable.
\(\frac{Change in cost}{Change in time}\) = \(\frac{20-10}{2-1}\) = \(\frac{10}{1}\) =10
\(\frac{Change in cost}{Change in time}\) = \(\frac{40-30}{4-3}\) = \(\frac{10}{1}\) =10
The rate of change for this situation is constant.

Question 3.
Miles a plane traveled while flying.
Spectrum Math Grade 8 Chapter 3 Lesson 1 Answer Key Understanding Slope 7
The rate of change for this situation is _____
Answer: The rate of change for this situation is constant.
The slope of a line on a coordinate grid can be found by determining the rate of change.
To find rate of change, divide the rate of change for the dependent variable by the rate of change for the independent variable.
\(\frac{Change in distance}{Change in time}\) = \(\frac{360-180}{40-20}\) = \(\frac{180}{20}\) =90
\(\frac{Change in distance}{Change in time}\) = \(\frac{720-540}{80-60}\) = \(\frac{180}{20}\) =90
The rate of change for this situation is constant.

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