Slope-Intercept Form Word Problems WKST | PDF | Fee | Teaching ... - Free Printable

Problem Analysis and Solution

The worksheet involves writing equations in slope-intercept form (\( y = mx + b \)) to model various real-world scenarios. Let's solve each problem step by step.

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#### Problem 1: Dancing Club
- Startup fee: \$30
- Monthly fee: \$4
- Slope-intercept form: \( y = mx + b \)
- Here, \( m \) is the monthly fee (\$4), and \( b \) is the startup fee (\$30).
- The equation is:
\[
y = 4x + 30
\]
where \( x \) is the number of months, and \( y \) is the total cost.

Answer for Problem 1:
\[
\boxed{y = 4x + 30}
\]

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#### Problem 2: Online Learning Community
- Startup fee: \$20
- Monthly fee: \$5
- Slope-intercept form: \( y = mx + b \)
- Here, \( m \) is the monthly fee (\$5), and \( b \) is the startup fee (\$20).
- The equation is:
\[
y = 5x + 20
\]
where \( x \) is the number of months, and \( y \) is the total cost.

Answer for Problem 2:
\[
\boxed{y = 5x + 20}
\]

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#### Problem 3: Library All-Star Members Club
- Sign-up fee: \$40
- Monthly fee: \$2
- Slope-intercept form: \( y = mx + b \)
- Here, \( m \) is the monthly fee (\$2), and \( b \) is the sign-up fee (\$40).
- The equation is:
\[
y = 2x + 40
\]
where \( x \) is the number of months, and \( y \) is the total cost.

Answer for Problem 3:
\[
\boxed{y = 2x + 40}
\]

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#### Problem 4: Total Cost for Library All-Star Membership (19 Months)
- Use the equation from Problem 3: \( y = 2x + 40 \).
- Substitute \( x = 19 \):
\[
y = 2(19) + 40
\]
\[
y = 38 + 40
\]
\[
y = 78
\]

Answer for Problem 4:
\[
\boxed{78}
\]

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#### Problem 5: Population of Florida
- Initial population in 2010: 17.4 million
- Annual increase: 0.22 million per year
- Slope-intercept form: \( y = mx + b \)
- Here, \( m \) is the annual increase (0.22), and \( b \) is the initial population (17.4).
- The equation is:
\[
y = 0.22x + 17.4
\]
where \( x \) is the number of years since 2010, and \( y \) is the population in millions.

Answer for Problem 5:
\[
\boxed{C}
\]

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#### Problem 6: Bike Rental Cost
- Base rental fee: \$4
- Hourly rate: \$1.50
- Slope-intercept form: \( y = mx + b \)
- Here, \( m \) is the hourly rate (\$1.50), and \( b \) is the base rental fee (\$4).
- The equation is:
\[
y = 1.50x + 4
\]
where \( x \) is the number of hours, and \( y \) is the total cost.

Answer for Problem 6:
\[
\boxed{y = 1.50x + 4}
\]

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#### Problem 7: Completing the Table for Bike Rental
- Use the equation from Problem 6: \( y = 1.50x + 4 \).
- Calculate \( y \) for \( x = 2, 4, 6, 8 \):

1. For \( x = 2 \):
\[
y = 1.50(2) + 4 = 3 + 4 = 7
\]

2. For \( x = 4 \):
\[
y = 1.50(4) + 4 = 6 + 4 = 10
\]

3. For \( x = 6 \):
\[
y = 1.50(6) + 4 = 9 + 4 = 13
\]

4. For \( x = 8 \):
\[
y = 1.50(8) + 4 = 12 + 4 = 16
\]

Completed Table:
\[
\begin{array}{|c|c|c|c|c|}
\hline
\text{Hours (} x \text{)} & 2 & 4 & 6 & 8 \\
\hline
\text{Total Cost (} y \text{)} & 7 & 10 & 13 & 16 \\
\hline
\end{array}
\]

Answer for Problem 7:
\[
\boxed{7, 10, 13, 16}
\]

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Final Answers:

1. \(\boxed{y = 4x + 30}\)
2. \(\boxed{y = 5x + 20}\)
3. \(\boxed{y = 2x + 40}\)
4. \(\boxed{78}\)
5. \(\boxed{C}\)
6. \(\boxed{y = 1.50x + 4}\)
7. \(\boxed{7, 10, 13, 16}\)