algebra teacher

PERCENTS: To find a percent increase or decrease is very easy, first for example if this is your problem : Find the percent increase or decrease from 110 to 440. First see if it is an increase or a decrease, you can see that it is an increase, so you have to find the amount of change and divide it bye the original number.   Keep in mind that you always have to subtract the smaller # from the bigger one. 440-110 divided by 110. 440-110 equals to 330, so divide 330 over 110 and that equals 3, but you have to make it a percent, so you move the decimal point 2 times and it will give you a 300 % increase. Do the same thing with the percent decrease. But always remember to subtract the smaller # from the bigger one.

440-110                                              330                             = 3= 300%

110                                                     110

TAXES and DISCOUNTS

For taxes and discounts it is really similar to finding a percent of a number, you first have to write you equation (if the problem is) original price= 20 dollars plus 7% of taxes, that equation will be written like this.

                                   7%        X

                                   _           _

                                100%      20$                          Multiply 20 x 7 and divide it by 100 and that will give you 1.4, after you have done all that you add your taxes to the original price and that will give you the total price(27$). You will do the same thing with the discount, but instead of adding it to the original price you will subtract, so if I gave you this problem, but 7% being the discount you will subtract it from 20 and it will give 13$.

FUNCTIONS

A function is a relationship between 2 mathematical elements (numbers). And for every input there is exactly 1 output if there is 2 then it is not considered a function.

            You can determine if something is not a function if there are 2 outputs for 1 input. For ex: 1,2 and 3,4 and 1,5 that is not considered a function, but if its written like this: 1,2 and 2,3 and 4,2 that is a function because 1 and 4 are different inputs.

VERTICAL LINE TEST: The vertical line test is a test to prove if an equation is a function, to do the test you graph your points and if you write a line that is vertical and 2 dots do not touch than your equation is a function.

            Domain and range: your domain in a function is (in your graph) what would be your X. For example: 2,1 and 3,6 and 4,1      your domains would be 2, 3 and 4 and your range would be 1 and 6(remember to write your domains and ranges in order and not to write them twice)

(REPRESENTATION ON PAPER)

SLOPES

To find the slope of the line that passes through 2 given points you have to look at your coordinates for ex these (1,2) and (2,3) you have to do the procedure like this:          y2-y1                         so basically     3-2 divided by 2-1 

                        _______

                        X2-X1             So your slope is 1. Because if you subtract it they both give you 1

To be able to read a slope is very easy, your slope is always going to be or look like a fraction, but don’t worry you just have to look at this problem like this. If your slope is 3 it will be         3            =        your Y                                                                                                                _                                                                                                                                          1    = your x and that is called rise(Y) over run (X)

HOW TO GRAPH AN EQUATION

To graph an equation you are given a y intercept and a slope, to graph that you first graph the y intercept, and to graph the next point you have to look at your slope, for ex if it is 3 you have to go up 3(y) and 1 to the right (x)                                               (Example on paper)

HOW TO WRITE EQUATIONS: STANDARD FORM First of all you have to know that on one side of the equation there has to be numbers with variables or variables and on the other side there has to be numbers without variables. Remember that your first variable has to be positive.(example on paper)                         SLOPE INTERCEPT FORM. For this equations remember the equation y=mx + b   That means y= your slope times X + your Y intercept.     Here is an example: y int= 4,   M=3     you write y=3x+4                                                                          POINT SLOPE FORM To write an equation in point slope form you may be given an equation written in slope intercept form, but you will always get to coordinate points, and a slope. For example : Write this (2,1) M=3 in point slope form. Your equation is like this                                                                                                        y-y1=M(x-x1)  so your equation will look like this                                                             y-1=3(x-2)

HOW TO DETERMINE IF 2 EQUATIONS REPRESENT PARALLEL OR PERPENDICULAR LINES                                                                                                                      If you are given two equations like these       y=3x+4 and  y=3/1x+1 you can notice that they are written in slope intercept form, and those lines are parallel, because if you notice they have the same slope so they are parallel, but to determine if a line is perpendicular you have to see that the slope is what is called a negative reciprocal, like there my slope is 3 the negative reciprocal would be -1/3. So in an equation is they have the same slope they are parallel lines and if it is the complete opposite they are perpendicular.