Writing and Graphing Equations in Two Variables

• 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

• 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

• 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

The graph will look like a "V"

f(x) = |x|​

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

Determining from a graph, table, and equation