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Back to Exercise: Use variables to represent two quantities in a real-world problem that change in relationship to one another

Use Variables to Represent Two Quantities in a Real-World Problem

Show your work. For word problems, write the equation first before building a table or plotting points.

Grade 6·22 problems·~35 min·Common Core Math - Grade 6·standard·6-ee-c-9
Work through problems with immediate feedback
A

Recall / Warm-Up

1.

Which quantity is the input (independent variable) in the statement: 'The number of miles driven depends on how long you drive'?

2.

In the equation y=4xy = 4x, which variable is the independent variable?

3.

Complete the table for the equation y=5xy = 5x. When x=0x = 0, yy =   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   . When x=3x = 3, yy =   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   . When x=6x = 6, yy =   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

y when x=0:
y when x=3:
y when x=6:
B

Fluency Practice

1.

A school printer prints 12 pages per minute. Which statement correctly identifies the independent and dependent variables?

2.

A taxi charges a flat fee of $3 plus $2 per mile.

The equation for the total cost cc in terms of miles mm is   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

The cost for 7 miles is   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

equation:
cost for 7 miles:
3.

A plant is 8 cm tall and grows 3 cm each week.

The equation for the plant height hh after ww weeks is   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

The height after 5 weeks is   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

equation:
height after 5 weeks:
Input-output table for d = 65t with four rows showing t values 0, 1, 2, 3 and empty d-value boxes to fill in.
4.

Complete the table for the equation d=65td = 65t (distance in miles, time in hours).
When t=0t = 0, dd =   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .
When t=1t = 1, dd =   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .
When t=2t = 2, dd =   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .
When t=3t = 3, dd =   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

d when t=0:
d when t=1:
d when t=2:
d when t=3:
Input-output table for e = 12h with four rows showing h values 0, 2, 4, 5 and empty e-value boxes to fill in.
5.

Complete the table for the equation e=12he = 12h (earnings in dollars, hours worked).
When h=0h = 0, ee =   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .
When h=2h = 2, ee =   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .
When h=4h = 4, ee =   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .
When h=5h = 5, ee =   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

e when h=0:
e when h=2:
e when h=4:
e when h=5:

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