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4.09 Modeling linear relationships

Interactive practice questions

After Mae starts running, her heartbeat increases at a constant rate.

a

Complete the table.

Number of minutes passed ($x$x) $0$0 $2$2 $4$4 $6$6 $8$8 $10$10 $12$12
Heart rate ($y$y) $49$49 $55$55 $61$61 $67$67 $73$73 $79$79 $\editable{}$
b

What is the constant rate the heart beat is increasing at?

c

Which one of the following equations describes the relationship between the number of minutes passed ($x$x) and Mae’s heartbeat ($y$y)?

$y=49x-3$y=49x3

A

$y=49x+3$y=49x+3

B

$y=3x-49$y=3x49

C

$y=3x+49$y=3x+49

D
d

In the equation, $y=3x+49$y=3x+49, what does $3$3 represent?

The change in one minute of Mae’s heartbeat.

A

The total time Mae has run.

B

The total distance Mae has run.

C
Easy
2min

A racing car starts the race with $150$150 liters of fuel. From there, it uses fuel at a rate of $5$5 liters per minute.

Easy
3min

In a study, scientists found that the more someone sleeps, the quicker their reaction time. The attached table shows the findings. Use a positive number to express increase, and a negative number to express decrease.

Easy
4min

Consider the points in the table below:

Easy
1min
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Outcomes

I.A.CED.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. 'Linear and exponential (integer inputs only)

I.F.IF.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

I.F.BF.1

Write a function that describes a relationship between two quantities.

I.F.BF.1.a

Determine an explicit expression, a recursive process, or steps for calculation from a context.

I.F.LE.5

Interpret the parameters in a linear or exponential function in terms of a context. Limit exponential functions to those of the form f(x) = b^x + k.

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