School is out, and you want to save money for a summer camp. You already saved \$25, and your parents will give you another \$25. You work part time, which will allow you to save $40 per week.

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In this lesson, you will use all three tools—equations, tables, and graphs—to analyze real-world relationships. Let's look at how each one can help you based on the information they show.












$f(x)=2x+1$

Strengths

  • You can use an equation to find the exact values of the independent and dependent variables.
  • It's easy to update the equation if changes happen in the scenario.
  • You can use the equation to make a table of values.

Limitations

  • It may be hard to visually see what the equation represents, especially if the equation is complicated.

$x$

$f(x)$

1

3

2

5

3

7

Strengths

  • You can quickly find the exact values.
  • You can use the table to make a graph.
  • It's easy to calculate the change in values for each variable.

Limitations

  • You will need to update the table if a solution isn't included in it.
  • If something changes, you have to update each value of the dependent variable.







graph

Strengths

  • It's easy to see the relationship between the two quantities.
  • It's easy to see the whole range of solutions.

Limitations

  • It might be difficult to find the exact values if the solutions are not whole numbers.
  • You will need to make a new graph if the situation changes.

Essential Questions

After completing this lesson, you will be able to answer these questions:

  • How do you use math tools to interpret, model, and solve real-world challenges?
  • What are the key features for a linear function, and how can you use those features to sketch graphs?
  • How do you change a linear function based on changes in the real world?