This week in math 10, we learned about the different form of equations and how to change between them.

Here are the different equations:

Slope intercept form

y=mx+b

Slope Point form

y-y₂=m(x-x₂)

General form

0=mx+y+b

 

Slope intercept form to Slope Point form (y=mx+b to y-y₂=m(x-x₂))

We want to take the equation y=4x+8 and convert it to slope point form. This is one of the most simple conversion.

The first step is to fin a point to convert: (0,8) being put into the slope changes to (1,12)

Next, you would just inster the number into the equation: y-12=4(x-1)

Slope intercept form to General form (y=mx+b to 0=mx+y+b)

This conversion is also very simple. All you need to do to subtract y:

y=4x+8

-y

0=4x-y+8

Slope Point form to General form (y-y₂=m(x-x₂) to 0=mx+y+b)

This conversion is a little more complicated. The first step is to convert form slope point form to slope intercept form:

We need to find the y-intercept, you can do that by applying the slope to the point in the equation: y-12=4(x-1) turn into y=4x+8.

You then can apply the conversion for Slope intercept form to General form.