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Angle Inclination of a Line - Problem 2

Teacher/Instructor Norm Prokup
Norm Prokup

Cornell University
PhD. in Mathematics

Norm was 4th at the 2004 USA Weightlifting Nationals! He still trains and competes occasionally, despite his busy schedule.

Let’s look at the problem that involves the angle inclination of a line here. Here I have a line with the equation 9x plus 4y equals 108. First where does the line cross the x axis so this is a little review. Where it crosses the x axis is at x intercept and that happens when y equals 0, so I just plug in 0 for y and I get 9x plus 4 times 0 equals 108 so 9x equals 108 and that means x equals 12.

So if I were to graph this and say this is the point x equals 12 that’s where it crosses the x axis. Now what’s the angle of inclination of L? In order to answer that question I would need to know its slope and so I’m going to put this in slope intercept form, so let me solve it for y first of all. 4y equals -9x plus 108 and then I just divide everything by 4. I get y equals -9 over 4 x plus 108 divide by 4 is 27. Well that’s my slope -9/4.

So to get from slope to angle of inclination, remember the tangent of angle of inclination equals slope so angle of inclination is inverse tangent of slope, in this case inverse tangent of -9 over 4. So let’s get an approximation for that on a calculator so inverse tangent -9 over 4 I get -66 degrees to the nearest degree. Now when you get a negative angle of inclination it means that the angle is measured clockwise from the positive x direction, so down this way, so say that.

Say that’s -66 degrees so I can easily draw the line if I have an accurately measured -66 degrees which and I know that’s very accurate but it’s good enough for a quick sketch. So you can use a point on the angle of inclination to sketch the graph of a line.

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