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Wize High School Algebra I Textbook (Common Core) > Relations & Functions

Relations

Solving Inequalities Involving Absolute ValuesPrevious Section
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Relations

Variables are letters such as xx, yy, tt, nn, that are used to keep track of quantities we want to measure or count. We are often interested in how two variables interact.


A relation describes how two variables are connected. We can represent a relation using words, a table, a graph, or an equation.



Independent variables: these are the values we choose; the values of the other variable in the relation depend on the value of this independent variable
Dependent variables: these are the values we calculate; they depend on the value of the independent variable

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Examples
  • An employee's daily pay VS the number of hours worked
  • Independent variable:
    hours worked
  • Dependent variable:
    amount of pay
  • The height of a tree VS the age of the tree
  • Independent variable:
    age of the tree
  • Dependent variable:
    height of the tree
  • The time a student spends studying VS their final exam grade
  • Independent variable:
    time spent studying
  • Dependent variable:
    final exam grade
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Graphing Points

When we have two variables like xx and yy, we sometimes want to plot their values on a graph on the Cartesian Plane (rectangular coordinates).


Notes
  • The horizontal axis is called the x-axis
  • The vertical axis is called the y-axis
  • Any point on the graph looks like (x, y)(x,~y), where the first number is the x-coordinate and the second number is the y-coordinate
  • We can plot the graph of any relation by plotting points on the graph and then connecting them
  • We ALWAYS "read" a graph from left to right, just like reading in English!
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Example: Relations

Create a graph and write an equation to represent the number of squares in each of the following patterns.

a)


Let nn be the "spot" in the pattern, and pp be the number of squares in the pattern.

Then, the equation representing the number of squares is p=3n\boxed{p=3n}.
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b)


Let nn be the "spot" in the pattern, and pp be the number of squares in the pattern.

Then, the equation representing the number of squares is p=3+2n\boxed{p=3+2n}.

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c)


Let nn be the "spot" in the pattern, and pp be the number of squares in the pattern.

Then, the equation representing the number of squares is p=n2\boxed{p=n^2}.

Practice: Table of Values & Graphs

Fill in the folllowing table of values for each equation, then create a graph based on that table of values.
y=2x−1y=2x-1
xy
-1
0
1
2