Compare Two Linear Representations

Compare two linear representations

When two linear representations describe the same quantity, you compare them by rewriting each one in a common form and checking whether they agree.

1) Identify the representation

A linear representation may appear as an equation, a table, a graph, or a verbal description. Look for the rate of change and the starting value.

2) Put them in a comparable form

If possible, rewrite each representation as an equation like: [ y = mx + b ] where:

• (m) is the slope or rate of change,
• (b) is the y-intercept or initial value.

For a table, find how much the output changes when the input increases by 1. For a graph, use two clear points to find the slope.

3) Compare the key features

Ask:

• Do the slopes match?
• Do the starting values match?
• Do the representations give the same output for the same input?

If both the slope and starting value are the same, the representations are equivalent. If only one matches, they are different.

4) Simplify your final answer

State the conclusion clearly and reduce any algebraic expression if the problem asks for one.

5) Check your work

Substitute a convenient input value into both representations. If both give the same output, your comparison is consistent.