Week 11 of Math 10 has us moving on from factoring trinomials to relations in mathematics. The second week of quarantine learning has been great so far, as I’ve been absorbing and understanding the topics well despite the limitations of online teaching. This blog post will be covering relations and how to express them in various forms.

A relation is a set of data that – as the name suggests – are related to each other. Some examples of relations include:

• The value of a vintage wine and its age
• The battery charge of a phone compared to how long its been plugged in
• Time to drive to a supermarket and distance

Relations are are comprised of two variables which are the independent variable and dependent variable. Although these can be renamed, these two values are commonly referred to as ordered pairs which is an X and Y value inside a parenthesis like (x , y). The independent variable which is X does not rely upon other values, whereas the dependent variable relies upon the independent variable to find the answer.

Relations can be represented in a variety of ways like with diagrams, words, sets of ordered pairs, but for this blog post I will be covering how to solve for x through equations and map them with a table of values

Our relation will be y=6x-2 and we’ll first start off by making a table of values to add them into.

To keep it simple, we will be using numbers 1-8 as our input values, in order to find the value of Y we have to solve the right side. So replace x with 1 and solve accordingly.

Now simply input the numbers into the X to solve for the output of Y.

Now that there’s a full table, you can actually turn these into ordered pairs, which can then be used for other diagrams like graphs.

And that’s how you solve relations.

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