Math 10 Week 13: The Many Forms of Equations for Slopes

There are three types of equations for slopes, Point slope form, Slope y-intercept form, and general form.

Point slope form is m(x-x2)=(y-y2).

Slope y-intercept form is y=mx+b.

General form is ax+by+c.

General form has an extra rule, A should always be positive.

Each form can be translated into the other except for changing other forms into point slope form (to my knowledge).

Let’s say the slope is 5, x2 is 4, and y2 is 3.

We start with point slope form and it will be changed into slope y-intercept form.

The best way to turn equations into y intercept form is to separate y from everything else, so the equation right now is 5(x-4)=(y-3).

To turn it to y intercept, you first want to multiply the slope (in this case 5) into the brackets next to it, so the equation is now 5x-20=y-3

Now, using algebra, we can add 3 on both sides to get y by itself, now the slope y intercept form is 5x-17=y.

Now, to change point slope form into general form, we do the first step again, to get 5x-20=y-3, this time, we move everything over, so we subtract y and add 3

Now the form should be in general form, the answer is 5x-y-17.

To change general form into y intercept form, all you need to do is move y over, so in this case, add y to both sides, and you will have your answer.

And that’s how to change forms between the 3 forms (excluding point slope form), next time we will talk about… systems to linear equations, or way to solve them. See ya next week!

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