Linear Equations

Example #1

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This is linear.

I can tell this is linear from the graph because the line is straight at all times.

I can tell this is linear from the equation because the variable has an exponent of 1, if variable has an exponent of anything except 1 it is non linear.

Example #2

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This is linear.

I can tell this is linear from the equation because the variables have an exponent of 1 attached to them, a non linear equation would have an exponent greater or less than 1 attached. All of the variables in an equation need to have an exponent of 1 for it to be linear.

I can tell this from the graph because the line is straight, even if it’s diagonal it is still linear.

Non-Linear

Example #1

This is non linear.

I can tell this is non linear from the equation because the variables in the equation have an exponent that’s not 1 meaning the equation is non linear.

I can tell this is non linear from the graph because it is not going in a straight line.

Example #2

This is non linear.

I can tell this is non linear from the equation because the 2 has an exponent that is not 1 meaning its a non linear equation..

I can tell this is non linear from the graph because the line is not straight, also something cool about this is although it may look like it’s touching the y axis in the negatives it never touches it.

Self Assessment

I explored Mathematical ideas using technology when I experimented with linear and non linear questions by graphing them on the Desmos app.

I analyzed data and used criteria to draw conclusions when I did a test to see if a non linear graph ever touched the line by zooming in but it did not. I also analyzed the data of other equations to see if they were linear or not.

I justified my conclusions with evidence when I gave reason to each of the 4 graphs on whether they were linear, or not and why.