Linear Equations:

The equation for this graph is 2x-3y=12, which means that this graph is linear because the equation for the graph follows Ax+Bx=C format, You can also tell that the graph is linear because it goes in a straight line.

The equation for this graph is y=1/3x-2, which means that the graph is linear because the equation for the graph is in y=mx+c format, You can also tell that the graph is linear because it goes in a straight line.

Non-Linear Equations:

The equation for this graph is y=square root x, Which means that the graph is not linear because the equation has root (exponent) in it and does not follow, y=mx+c or Ax+Bx=C, You can also tell that the graph is not linear because it does not go in a straight line.

The equation for this graph is y=(x+1)(x+1), which means that it is not linear as it ends up having exponents, and does not follow y=mx+c or Ax+Bx=C, You can also tell that this graph is non-linear because it does not go in a straight line.

How to make the Non-Linear equations Linear:

For the equation, y=square root x, you can make the equation linear by removing the exponent, (square root).

For the equation, y=(x+1)(x+1), you can make the equation linear by removing the brackets (x+1) and making it y=x+1

self-assessment:

I explored mathematical ideas using technology when I looked at the different ways the graphs turned out by changing the values in the equation.

I analyzed data and used criteria to draw conclusions when I was proving whether or not the equation was linear or non-linear I used the data given from the graph, and the equation to look and see if any of them followed the correct equation or went in a straight line.

I justified my conclusions with evidence once I figured out if the equations were linear or nonlinear, and I showed how you could reformat the non-linear equations and remove exponents, powers, and square roots to make the equation work as a linear equation.