Writing and Graphing Equations in Two Variables

Equations With Two Variables

Follow this lesson to learn about graphs that have two variables or unknowns in the equations. This lesson will use tables, graphs, and equations to determine values and information.

Two Variable Equations

• Consider p = $11.50h

• H: INPUT or INDEPENDENT variable because it does not stand alone. It is multiplied by a real number in this case $11.50

• P: OUTPUT or the DEPENDENT variable and stands by itself

• These variables can be put into an ORDERED PAIR (h, p)

• These equations can be visualized as a mathematical equation, a table, or a graph

Equations as Functions

• Written as f(x)=11.50x

• f(x) can be thought of as y

• To be a FUNCTION the equation must have one output value for each input value

• Watch this video to see graphing by using tables and how to determine if they are functions

• Next answer a few questions

Multiple Choice

Find the 2 missing OUTPUT values.

• 6 & 12
• 4 & 12
• 4 & 2
• 6 & 2

Multiple Choice

Name the DEPENDENT variable from the table below.

• minutes
• bubbles

Multiple Choice

Name the INDEPENDENT variable from the table below.

• words
• minutes

Multiple Choice

Which axis runs horizontally?

• x
• y

Multiple Choice

Which axis runs vertically?

• x
• Y

Multiple Choice

How would I graph the point (-1, 3)?

• Left 1, up 3

• Left 1, down 3

• Down 1, Right 3

• Down 1, Left 3

Multiple Choice

Which table is correct for y=4x+3?

Types of Graphs

• Usually you can plot 4 - 5 points especially when both variables are to the first power

• When the equations contain variables with exponents other then 1, absolute value bars, or square root symbols it is better to plot 8-9 points

• Connect the points with a smooth curve

• Equations that are straight lines are referred to as LINEAR

• All other equations are referred to as NON-LINEAR

ABSOLUTE VALUE EQUATIONS

The graph will look like a "V"

f(x) = |x|​

QUADRATIC EQUATIONS

The graph will look like a U that is called a parabola

f(x) = x²​

The graph looks similar to an 'S'.

f(x) = x³​

​

Cubic Equations

This graph looks like an arc

f(x) = √ x​

​

​Square Root Function

Linear Vs. Non-Linear

Determining from a graph, table, and equation

Multiple Choice

Determine if the graph is linear or nonlinear.

• Linear
• Nonlinear

Multiple Choice

Is the function Linear or Nonlinear?

• Linear
• Nonlinear

Multiple Choice

Is the equation linear or nonlinear?

• Linear
• Nonlinear

Multiple Choice

Is the equation linear or nonlinear?

• Linear
• Nonlinear

Multiple Choice

Is this function linear or nonlinear?

• Linear function

• Nonlinear function

Multiple Choice

Is the representation linear or non-linear? 

• Linear
• Non-Linear

Multiple Choice

Is function represented by the table linear or nonlinear?

• linear
• nonlinear

Multiple Choice

From the table, is the function Linear or Nonlinear?

• Linear
• Nonlinear

Multiple Choice

Name the parent function.

• quadratic

• cubic

• square root

• logarithmic

Multiple Choice

What type of function is shown?

• absolute value

• quadratic

• linear

• exponential

Multiple Choice

• cube root

• cubic

• quadratic

• logarithmic

Multiple Choice

• linear

• cube root

• square root

• quadratic

Multiple Choice

• quadratic

• absolute value

• square root

• inverse

Poll

How do you feel about the lesson?