Hello all, hope you are enjoying your evening.
Got home a little early from work and began my maths work. Since I had more time, I didn’t feel pressured to get some done plus write up a reflection of the session.
Continuing from yesterday, in the middle of the “Equations of Lines” part, I finished off the different equations for lines and ended it with the “general linear equation”.
5 equations exist for the line.
Careful considerations are needed for the slope of the vertical and horizontal lines:
Vertical: Slope is undefined.
Horizontal: Slope is defined as zero.
I copied the examples into my notes, took screenshots of the important information and attempted the practice problems.
A switch up from yesterday was to use Desmos, an online graphing calculator. Handy to use if you don’t have a physical graphing calculator (plus it doesn’t cost anything to use compared to a calculator!).
It is an elegant app, which all you do is plug in the equation and it spits out the result (as long your equation is correct). Here is an example (y = 3 x + 5):
And when you save it, it produces the image below:
Nice and easy. Less cumbersome than coding it.
I will still be learning Julia, but it’ll likely happen when Desmos becomes less useful (such as annotating and labeling).
However, I found a GitHub page containing information on Julia and how to use it in different circumstances, including for use as a graphing calculator. The pages were developed by College of Staten Island for their MTH229 course. Seems like it contains useful information on using Julia for maths - I will explore this at a later date.
At this point, with most of the equations graphed, I began to check my answers against the book.
Pretty good so far….then I hit the final question…
First of all, mixed 2 for 12 (which produces the -36 instead of -6). And then I messed up on how to write the equation.
The question gives you the equation of the line in linear form, however I implicitly converted it to the slope-intercept form (which is the form you want the answer to be in) without properly following the process.
In this case, you’re meant to rearrange it to solve for y (since the final answer needs to be in the slope-intercept form), i.e subtracting x and then dividing each side by -3.
By the end, it should look like this:
It’s amazing how a little error in your writing can produce a vastly different result.
This mistake, also, tells me that I got to work on my algebra a bit more (until it’s second-nature) and to pay a bit more attention to what I’m doing.
But with this mistake fixed up and understood, it is time to complete the exercises. I just checked, there are 80 questions plus questions within some of those. This is great practice!
But that is all for tonight, I hope you enjoyed reading this as I have writing on my reflection. I hope to see you in the next study session!
Steve Frampton.