Linear & Non-Linear Equations &

GraphsWhat do they look

like?

• The LINEAR EQUATIONS usually look like these

y = xy =2x

y = 2x – 1y = -5x + 2

Linear Equations

•Let’s list what they have in common!

y = xy =2x

y = 2x – 1y = -5x + 2

Linear Equations

Linear Equations•These equations have a “y” and an “x”

•The exponent on the X is “1”

• Let’s list what’s different about them!

y = xy =2x

y = 2x – 1y = -5x + 2

Linear Equations

Linear Equations•The number in front of the x can be different

•We can add or subtract any number

• Let’s look at linear graphs on the board with their equations.

•What do we notice about them?

Linear Graphs

• Linear equations graph as LINES!

• The lines can start at the origin or above or below it.

• The lines can be steep or low

• Lines can be vertical or horizontal too

Linear Graphs

Non- Linear Equations• Non-linear equations are any

equations where the exponent on x is NOT “1” or absolute value

y = x2

y =2x3

y = |-5x + 2|1– 2x y

• Let’s look at non-linear graphs on the board

•What do we notice about them?

Non-Linear Graphs

•Non-linear equations form graphs of all shapes and curves, BUT NOT LINES!!!

Non-Linear Graphs

• The Most Popular Non-linear graphs are:

• QUADRATIC y = x2

• The graph is a parabola

Non-Linear Graphs

or

• CUBIC y = x3

• The graph is like this:

Non-Linear Graphs

or

• ABSOLUTE VALUE

• y = |x|

• The graph is like this:

Non-Linear Graphs

or