Question 466497: Beginning & Intermediate Algebra: Please explain in simple terms, what does the addition/subtraction and multiplication/division properties means?
How do I know what to substract or add in linear equations?
Which number to add or subtract on both sides and how do I know when to do either?
Also what is the definition of a slope on a graph?
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! 1. The four basic arithmetic operators have certain properties, i.e. addition and multiplication are commutative; e.g. a+b = b+a and a*b = b*a for all a,b. Subtraction is not commutative but it is sometimes referred to anticommutative, because a-b = -(b-a) for all a,b. Division doesn't hold either of these properties.
For the second and third questions you just have to be familiar with equations, and that takes practice. In order to solve for a variable in a linear equation such as 5x + 3 = 13, you should generally isolate the variable from the rest. Here you subtract 3 from both sides, leaving 5x = 10, divide both sides by 5 to get x = 2.
For the fourth question, slope is defined as rise over run; i.e. the "steepness" of the graph (but not quite). If you have two points you can find the slope by taking the change in the y-coordinates and dividing it by the change in the x-coordinates.
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