Question

1. use the information below to answer the following questions.

a)
circle discrete or continuous
the independent variable is _______________
the dependent variable is _______________
is this a linear relation? how do you know?
b)

# of containers	total mass (t)
5	19.5
6	21
7	22.5
9	25.5

circle discrete or continuous
the independent variable is _______________
the dependent variable is _______________
is this a linear relation? how do you know?

1. complete the table of values below assuming the data represents a linear relation

x	y
5	30
7
9
	60

Explanation:

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1a)

Step1: Classify variable types

Age and heart rate can take any value within a range, so continuous (circle this).

Step2: Identify independent variable

Independent variable: Age (it is the input variable).

Step3: Identify dependent variable

Dependent variable: Maximum heart rate (depends on age).

Step4: Check linearity

The graph is a straight line, so it is linear.

Step1: Classify variable types

Number of containers is a whole number (counted), so discrete (circle this); total mass is continuous, but the independent variable defines the classification here.

Step2: Identify independent variable

Independent variable: # of containers (input variable).

Step3: Identify dependent variable

Dependent variable: total mass (depends on container count).

Step4: Check linearity

Calculate the rate of change:
$\frac{19.5-18}{5-4}=1.5$, $\frac{21-19.5}{6-5}=1.5$, $\frac{22.5-21}{7-6}=1.5$, $\frac{25.5-22.5}{9-7}=1.5$. The rate of change is constant.

Step1: Calculate slope

Use points $(1,10)$ and $(5,30)$. Slope $m=\frac{30-10}{5-1}=\frac{20}{4}=5$.

Step2: Find linear equation

Use $y=mx+b$. Substitute $x=1, y=10, m=5$:
$10=5(1)+b \implies b=5$. Equation: $y=5x+5$.

Step3: Solve for missing values

• For $x=3$: $y=5(3)+5=20$
• For $x=7$: $y=5(7)+5=40$
• For $x=9$: $y=5(9)+5=50$
• For $y=60$: $60=5x+5 \implies 5x=55 \implies x=11$

Answer:

Circle: continuous
The independent variable is $\boldsymbol{Age}$
The dependent variable is $\boldsymbol{Maximum\ heart\ rate}$
Yes, it is a linear relation. The graph is a straight line.

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1b)