Algebra: Chapter 7, Lesson 1 and Lesson 2, pages 304 and 309
Chapter 7-1 Coordinates
Coordinates are defined as `(x, y)` where the x-axis runs left to right and the y-axis runs up and down. The origin is where the points `(0, 0)` exists. A fancy word for the x-axis is the abscissa and the y-axis is the ordinate. There are 4 quadrants:
- I – both x and y axis have positive value (upper right)
- II- x axis is negative and y axis is positive (upper left)
- III – both x and y axis have negative values (lower left)
- IV – x axis has positive value, while the y axis has negative value (lower right)
By substituting a coordinate pair `(x, y)` into a linear equation, we can determine if the ordered pair is a solution to the linear equation. Just substitute for `x` the value of the first of the ordered pair, and substitute for `y`, the second value of the ordered pair. If the evauation is true, then the ordered pair fits on the line.
Chapter 7-2 Graphing Equations
We can graph an equation, by building a T-chart of values for both x and y. You can choose any values for `x ` and `y` when making your T-chart. I like to use values like 0, 1, and 2. Make them easy and try to pick AT LEAST 3 points when graphing and equation. YOU MUST USE A RULER WHEN CONNECTING THE DOTS TOO!
Sometimes, it can be easier when building the T-chart to “solve for y” first, this just cuts down on the workload. Solving for y means isolating the y variable to one side of the equation and keeping the constants and ALL other variables on the other side.
Here are 2 good links from purplemath.com, the first about graphing in general (lesson 7-1) and the second about the T-charts and lesson 7-2!