Linear Equations

This is a linear equation. I can tell from this graph that is a linear equation because the graph is a straight line. I can tell from the equation that this is a linear equation because it is in the y=mx+b format, just in a different sequence.

This is also a linear equation. I can tell from the graph that it is a linear equation because it forms a straight line. I can tell from the equation that it is a linear equation because it follows the y=mx+b format. Because there are no exponents and the rest of the equation follows the y=mx+b format, this equation is linear.

Non-Linear Equations

This is not a linear equation. I can tell from the graph that it is not a linear equation because the line curves. I can tell from the equation that it is not a linear equation because it does not follow the y=mx+b format. Because x is an exponent attached to the number 2 and has no additives, it is not a linear equation.

This is not a linear equation. I can tell from the graph that it is not a linear equation because the graph is not a straight line. I can tell from the equation that it is not a linear equation because the equation doesn’t follow the y=mx+b format. Because it does not have an addition attached to the X and instead has an exponent, it is not a linear equation.

Self Assessment

I explored mathematical ideas using technology when I used Desmos graphing calculator to graph equations. I analyzed data and used criteria to draw conclusions when I looked for evidence within the graphs and equations to determine whether they were linear or non-linear. I justified my conclusions with evidence when I explained whether the equations followed the y=mx+b format and were a straight line to prove if they were linear or non-linear.