Linear Equations

This is a linear equation. I can tell from the graph because it is a line, linear equations are straight lines going in any directions, some of them are linear functions, this one isn’t however because it has a repeating x value. I can tell from the equation, because, this equation dose not have an exponent higher than one, if it did the line would be curved and then it would not be a linear equation.

This is a linear equation. I can tell from the graph because, it is a straight line, in this case, it is also a linear function, a one-to-one function as well, because this straight line has no repeating x or y values. I can tell from the equation, because there is no exponent greater then 1.

Non-Linear Equations

this is not a linear equation. I can tell from the graph because this is not a straight line, it is curved, however while not a linear equation, it is still a function, because it has no repeating x values. I can tell from the equation, because, while there is no exponents higher then one on the original question, y = (x+1) (x+1) can be rewritten to y = (x+1)^2, in which the question now has an exponent higher then one.

This is not a linear equation. I can tell from the graph because this is not a straight line linear equations have to be straight, however it is still a function because it has no repeating x values I can tell from the equation, because there is an exponent higher then one in this equation.  

Self-Assessment

• I explored mathematical ideas using technology when I used Desomos to graph the equations showing the difference between linear and non-linear equations.

• I analyzed data and used criteria to draw conclusions when I discussed if each of the above graphs were in fact linear or non-linear equations.
• I justified my conclusions with evidence when I used my knowledge of linear, and non-linear equations to use corresponding graphs, that justified my conclusions about them.