C: I was very intrigued with your exposition of a
linear relationship using the
concept of proportionality.
This is not how it’s traditionally taught in schools (at least where I’m from),
but your approach appears easier to follow.
R: Thanks! The definition of linearity in that post is equivalent to the traditional definition. In fact, our definition basically spells out the equation of straight line in 2-D. We’re glad that you agree that our definition is a more intuitive way to understand a linear relationship.
C: I loved the visualization
of income and expenses on the net worth (NW) scale.
Now it’s more clear to me how income and expenses fit into the bigger picture.
R: Thank you, we’re glad you find the visualization helpful. In upcoming posts, we’ll build upon this visualization to show how NW evolves over time due to factors other than income and expenses, so stay tuned!
Q: The analogy between percentage and decimal number system
is very interesting!
I know that the reason for having base 10 is due to us humans having 10 digits,
but what’s the reason for basing percentages on 100, instead of, say 10?
A: The base of 100 for percentage is purely by convention. Computationally, it’s also convenient to use 100 (in the decimal number system) since it’s a power of 10, i.e., $100=10^2$. So for example, multiplication or division of a number by 100 simply involves shifting the position of the decimal point in that number by two positions to the right or left respectively.
Q: You showed how a graph can be used interchangeably with a formula in the
variables and graphs post.
While I can see how to use a formula for any value of the variable, how can I
use the graph for a value that’s outside the range of that’s shown in the
graph, say 1000 CAD?
A: Good question! In this case, you’d simply extend the line that represents the CAD-MXN graph to the desired range, i.e., until at least the point representing 1000 CAD on the X-axis, and then follow the same procedure outlined in the post to get the corresponding value of MXN.
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Legend: Q => Question | A => Answer | C => Comment | R => Response ↩︎