9F Two-Variable Relationships Study Guide

Key Vocabulary

Independent Variable — the variable you choose or control (x); it does not depend on anything else. (variable independiente)

Dependent Variable — the variable that changes based on the independent variable (y); it depends on x. (variable dependiente)

Equation — a math sentence showing two expressions are equal (y = 3x + 2). (ecuación)

Table — a chart that organizes input-output pairs in rows. (tabla)

Graph — a visual display of ordered pairs plotted on a coordinate plane. (gráfica)

Relationship — how two variables are connected by a rule. (relación)

Input / Output — the value you put in (x) and the value you get out (y). (entrada / salida)

Situation: A movie ticket costs $8 each.

Step 1: Table

Step 2: Equation

y = 8x

x = number of tickets (independent)
y = total cost (dependent)

Step 3: Graph

  y (cost)
 32 |            *
 24 |        *
 16 |    *
  8 |*
    +---+---+---+--- x
    0   1   2   3   4
        (tickets)

1 Identify the independent (x) and dependent (y) variables. Ask: "Which variable do I choose? Which one changes because of my choice?"
2 Write the equation that relates x and y. Look for a pattern: what do you do to x to get y?
3 Make a table of values. Pick several x-values, apply the rule, and write the y-values.
4 Graph on the coordinate plane. Plot each (x, y) pair and connect the points if the relationship is continuous.

y = mx (y equals a number times x)

y = mx + b (y equals a number times x, plus a starting value)

m = how much y changes for each increase of 1 in x | b = starting value when x = 0

Independent = what you CHOOSE. Dependent = what CHANGES because of it. Don't mix them up!
Label your axes! x-axis = independent variable, y-axis = dependent variable.
The equation must work for ALL rows in the table, not just one.
On a graph, the independent variable is always on the horizontal (x) axis and the dependent variable is on the vertical (y) axis.

1. A babysitter earns $12 per hour. Using the equation y = 12x, how much does she earn in 5 hours?

2. Look at this table:

The rule is y = 3x + 2. What is y when x = 4?

3. In the equation y = 7x, which is the independent variable?
Type "x" or "y".

4. A car travels 55 miles per hour. Using the equation d = 55t, how far does it travel in 3 hours?