Linear & Non-Linear Equations & Graphs What do they look like?

The LINEAR EQUATIONS usually look like these y = x y =2x y = 2x – 1 y = -5x + 2 Linear Equations

Let’s list what they have in common! y = x y =2x y = 2x – 1 y = -5x + 2 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 = x y =2x y = 2x – 1 y = -5x + 2 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 = x 2 y =2x 3 y = |-5x + 2|

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 = x 2 The graph is a parabola Non-Linear Graphs or

CUBIC y = x 3 The graph is like this: Non-Linear Graphs or

ABSOLUTE VALUE y = |x| The graph is like this: Non-Linear Graphs or