Linear and Non-Linear Equations

Linear Equations

x=4

This is a linear equation. I can tell from the graph because the equation forms a straight line. I can tell from the equation, because it is a polynomial and has whole numbers.

y – 3 = 4(x+1)

This is a linear equation. I can tell from the graph because the line on the graph is not curved but straight. I can tell from the equation, because it does not have a degree over 1 and only contain whole numbers.

Non-Linear Equations

y=-2(x-4)^2

This is not a linear equation. I can tell from the graph because the line is curved. I can tell from the equation, because it contains exponents.

y= 1/2 x^3

This is not a linear equation. I can tell because of the line being curved. I can tell from the equation, because it contains numbers that are not whole.

Self-Assessment

I explored mathematical ideas using technology when I further researched the differences between linear and non-linear equations to be able to better understand them. This allowed me to answer the questions in full sentences and proper reasoning.

I analyzed data and used criteria to draw conclusions when I was determining which equations were linear and non-linear. I used the information I already had and was able to distinguish the differences.

I Justified my conclusions with evidence when I used reasoning and information that was in the equations to prove my points. I also justified my conclusions with the graphs by stating that non-linear equations are curved.