The Science of Life Lecture Series

Hello internet, and welcome to the Algebra Lecture Series from The Science of Life.  This entry is an introduction to Linear Functions in both graphs and models. There are two situations where the slope would not be stated in the slope-intercept form.  These are cases where the line crosses only one of the 2 (or more) axes. First, let's consider the horizontal line.  If we have a line which has a y-intercept but does not have an x-intercept (does not cross the x-axis), it is called a horizontal line.  Let's look at it from the point of view of the slope-intercept form we developed last time, $y=mx+b$.  We know that the slope is the change in the y-value per change in the x-value.  If we have two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$, the slope is mathematically defined as $m=\frac{y2-y1}{x2-x1}$.  The denominator, the $ dx=x2-x1$, is never going to be zero when there's a y-intercept, since we can go from the left of the y-intercept to th...

If you're familiar with a number line, then you know that each point on that number line corresponds to a number.  If we take two number lines which are perpindicular to one another (they cross each other to make a right angle) and have them cross at the others zero-point, then we have a method of analyzing two-dimensional data-sets and equations, data and equations with two variables which relate to one another.  This two-number-line situation is typically called either the x-y coordinate system (because the horizontal number line is labeled as the x-number line and the horizontal is labeled as the y-number-line) or the Cartessian Coordinate System (named after French mathematician René Descartes, supposedly the first person to come up with the system).  The two number lines, since they're in the context of a coordinate system, are each now called an axis (plural: axes). The x-axis and y-axis of a Cartesian coordinate system. Any point on this coordinate system i...

Graphs are an important part of Algebra since they allow us to visualize information from the equations of Algebra.  After all, we deal better with the visual than the equation.  When we have an equation of two variables, we can see how they relate to one another more readily in a graph than in an equation. The course of Algebra focuses on the concept of functions (which will be defined in Section 2; because yes, functions are different than equations).  Most of the graphs considered here are what is called linear equations, equations which produce lines.  This chapter has the purpose of not only teaching the basics of graphing functions, but also using them for problem solving. Section 1: Graphs Section 2: Functions Section 3: Linear Functions: Graphs and Models Section 4: Other Equations of Line Section 5: Other Equations of Lines Section 6: The Algebra of Functions That's the end of this section.  If you have any questions, please leave ...

Hello internet, and welcome to the Algebra Lecture Series from the Science of Life.  This entry is an introduction to algebraic problem solving.  In Algebra, there are five steps for problem solving, which I'll cover here. Familiarize yourself with the problem situation.  This is basically a situation of knowing what the context of the problem is.  Is the context taxes?  Grocery shopping?  Tipping?  Scaling up or down the ingredients of a cake to get a different size cake than what the recipe says the size will be?  Here are the sub-steps for this contexts step: Read the problem carefully.  Read it aloud if need be to understand the problem. List the information and state the question being asked.  Select variables to represent anything which is unknown and clearly state what the variables represent, and be descriptive about the statement. Obtain any relevant information and equations.  If you're painting a room, find the ...