The Science of Life Lecture Series

Hello internet, and welcome to the Algebra Lecture Series from The Science of Life.  This entry is focusing a little deeper into the concept of lines, especially the other equations of the line. Suppose that we have a line with slope $m$ and it passes through a specific point $(x_{1}, y_{1})$.  For any other general point (x, y) on the line (where $x_{1} \neq x$ and $y_{1} \neq y$) on the line, the slope of the line would be $m=\frac{y-y_{1}}{x-x_{1}}$.  Multiplying both sides of the equation by the denominator of the right hand side gives us $m \times (x-x_{1})=(y-y_1)$.  This final form is called the point-slope form of the linear equation, since we use a point and the slope. The two green lines are parallel. If we look at two parallel lines, they do not cross (they have no solution) by the definition of parallel lines.  This can only be done if the change in the y variable (the rise) for every unit change in the x variable are exactly the same ...

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 ...