Taylor's Blog 6(or 7 or 5 i don't know lol XD)

These are my notes from 8.2 on how to find the angle of inclination of a line.

This is the formula that you need to find the angle of inclination of a line.

m= tan alpha You use this formula when you are given a line. It is also used to find the inclination of that line.

(REMEMBER I DO NOT KNOW HOW TO PUT A GRAPH ON HERE SO PLEASE NOTE THIS. WHEN I SAY DRAW A QUARDNENT PLANE DO SO AND CHECK THE ONES THAT I TELL YOU TO OK!!)

Now lets work on a problem!!!

Find the angle of inclination for the line y= 5/8x+ 4.

y= 5/8x+ 4 First, write the equation down.

5/8= tan alpha Since, you are trying to find the angle of inclination for a line you would you the first formula that I gave you and put it like this.

alpha= tan ^-1(5/8) Then you need to put it in inverse form like I did.

alpha= 32.003 degrees Then you simply need to find the inverse and round the decimal to the hundredths place. Ok, now draw you quadrant plane. Now since our tan is positive we need to put a check in the quadrants where tan or X and Y would be positive. Which is the First and Third Quadrant. So since we have the First Quadrant already we just need to find the Third Quadrant.

32.003 degrees + 180 degrees = 212.003 degrees Finally you just add 180 degrees to find the Third quadrant.

Your answers should be alpha= 32.003 degrees and 212.003 degrees.

Lets try one more example!

Find the angle of inclination for the line y= 3/5x+ 7.

y= 3/5x+ 7 First, write the equation down.

3/5= tan alpha Since, you are trying to find the angle of inclination for a line you would you the first formula that I gave you and put it like this.

alpha= tan ^-1(3/5) Then you need to put it in inverse form like I did.

alpha= 30.964 degrees Then you simply need to find the inverse and round the decimal to the hundredths place. Ok, now draw you quadrant plane. Now since our tan is positive we need to put a check in the quadrants where tan or X and Y would be positive. Which is the First and Third Quadrant. So since we have the First Quadrant already we just need to find the Third Quadrant.

30.964 degrees + 180 degrees = 210.964 degrees Finally you just add 180 degrees to find the Third quadrant.

Your answers should be alpha= 30.964 degrees and 210.964 degrees.


That is what I learned and my notes on how to find the angle of inclination of a line from lesson 8.2.