Algebra: Chapter 7, Lesson 1 and Lesson 2, pages 304 and 309
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.
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!
Two of tonight’s homework problems solved by MrE are here! Just click it
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Algebra 1a : Chapter 3, Lesson 4, page 130
Using the Properties Together
You can solve these equations in a variety of ways. Remember the objective is to ISOLATE the variable on one side. You can add, subtract, multiply or divide the same thing on both sides of the equation.
Follow these 4 steps:
- you should solve equations with parenthesis using the distributive property
- if there are like terms on one side of the equation, collect those first.
- add and subtract the constants
- finally, multiply or divide by the coefficient (next to the variable) to isolate the variable
Practice makes perfect and be sure to SHOW ALL THE STEPS! Purplemath has some examples here about these multi-step equations.
Don’t forget to use the reciprocal, its sometimes the same as dividing but faster.
DO NOT TAKE ANY SHORTCUTS, SHOW ALL THE WORK IN ALL ITS GORY DETAIL, THIS WILL REALLY SAVE YOU IN THE LONG RUN BY CUTTING DOWN ON SILLY MISTAKES!!
Expressions and Equations
The phrase the quantity suggests a grouping of terms will follow. The words sum of, difference of , product of and quotient of also suggests a grouping of terms (USING PARENTHESES) to follow.
The quantity “3 less than a number” is written `n−3`. The text “4 times the quantity 3 greater than a number” is translated to `4(n+3)`.
Finally, here are some problem-solving guidelines:
Phase 1: UNDERSTAND THE PROBLEM
- What am I trying to find?
- What data am I given?
- Have I ever solved a similar problem?
Phase 2: Develop and carry out a PLAN
- What strategies might I use to solve the problem?
- How can I correctly carry out the strategies I select?
Phase 3: Find the ANSWER and CHECK
- Does the proposed solution check?
- What is the answer to the problem?
- Does the answer seem reasonable?
- Have I stated the answer clearly?
Two of tonight’s homework problems solved by MrE are here! Just click it