Week 5 – Sept. 30th to Oct. 6th

In Week 5 I was able to start and finish two units, Linear Equations and Inequalities and Graphing Lines and Slope. As the names would suggest, this week I spent all of my time learning more about graphs and how to determine where to draw a line and its slope based on a given equation on a graph.

In the unit Linear Equations and Inequalties I learned that:

  • A Linear Equation is an equation that is graphed as a straight line, hence the word LINE in linear (ex. y = 2x +1 and 4x – 3y = 12). 
  • A Non-linear Equation would be any equation that does not result in a straight line (ex. y = x^2 and xy = 12 and 5/x + y = 10).
    • RULE: If both sides of an equation have only constants (i.e. whole numbers) and/or a constant to the first power of a variable (ex. 2x or 4y, i.e. 2x^1 and 4y^1), and you’re not multiplying or dividing variables, it is a linear equation.
  • The X-Intercept is the point on a graph where the line intersects the X-axis when y = 0 (ex. (6,0) or (3.5, 0)).
  • The Y-Intercept (denoted using the variable “b”) is the point on a graph where the line intersects the Y-axis when x = 0 (ex. (0, 6) or (0, 2.823764)).

In the unit Graphing Lines and Slope I learned:

  • Slope = m = increase-in-verticle/increase-in-horizontal = rise/run = change-in-Y/change-in-X = y[2] – y[1]/x[2] – x[1].
    • “Change-in” can be denoted by using a small triangle, called “delta”, in front of the variable y, x, etc.
    • If the slope (m) equals:
      • 1 (i.e. y = 1x + 2) the line has an upward 45 degree angle,
      • >1 the line has a >45 degree angle,
      • <1 but >0 the line has a <45 degree angle,
      • 0 (i.e. no slope) the line is horizontal,
      • -1 the line is a downward 45 degree angle,
      • <0 but >-1 the line has a downward <45 degree angle,
      • <-1 the line has a downward >45 degree angle.
  • Slope Intercept Form is one of if not the most widely used equations for determining the line on a graph. It’s written as y = mx + b (ex. y = 2x + b).
    • SIF make it easy to see the slope (m) and Y-intercept (b).
  • If the change-in y = 0, the line is horizontal and m = 0.
  • If the change-in x = 0, the line is vertical and m = undefined.

Going forward, there are four more units in the Algebra Basics course. My goal is to get through all four in Weeks 6 and 7. The next unit, Systems of Equations looks relatively small and the following unit, Epressions with Exponents, is already ~90% completed so it should definitely be doable. Now if I could just figure out how to have the rest of the work in my life ~90% finished before I started I’d be set.