This week I learned about arithmetic sequences, more specifically what terms are and how they are related to the numbers in sequences. First off arithmetic sequence means that the pattern of numbers all go up by the same amount each time. The first number of a arithmetic sequence is called term 1, the second number is term 2, and so on… You can be able to find the pattern or common difference of the sequence with the multiple terms listed. Once the common difference is found then you multiple that by each term to find out how much you need to add or subtract to get the final equation.
This week I learned what elimination was in the sense of applying it to systems of equations. For elimination to work you would need to 2 equations on top of one another as if it looks like you’re going to add them (you are). First you would need a zero pair which means both equations have to have either the x or y value be opposite from each other like -5 and 5. Once you have a zero pair, cross it out add all the other numbers. If there isn’t already a zero pair, you would need to make one by multiplying one of the equations to equal a zero pair to the other.
This week in math I learned what substitution for linear equations were. Substitution as you may already know is when you take something out and replace it with something else. In math we did that with equations. First we start off with 2 equations and choose which one to rearrange so either x or y equals to something. Then input the rearranged equation into one of the other equations’ variables in brackets then solve. Once you’ve found the answer, input that into the rearranged equation and you should get the other variable’s answer. Once completed verify the solution.
This week I learned about different forms of writing slope and y-intercept equations and being able to graph them. One specific one I’m going to talk about this week is point-slope form. Point-slope form is what I would consider and many others to be the most useful form because you’ll be able to branch off of that one to get to the other forms (general and slope y-intercept). Point slope form requires knowing the slope and a pair of coordinates/ordered pairs, from there you would subtract the y value from y and insert an equal sign and on the other side put the slope and in brackets to indicate multiplication, insert the x value subtracted from x.
This week I learned how to calculate distance and slopes for a line on a graph. To calculate the slope of a line you would need to take the y values from each point and subtract them from each other, then do the same for the x values. Then you put the difference over the sum and that should give you the slope. To determine whether the slope is positive or negative is noticing which way the line goes, reading the graph from left to right. If the line starts higher going down it’s negative, but if the line starts lower going up, it’s positive.
This week I learned what function notation was. Function notation is a equation where you can input a number and the output will come out the other side. From the left side of the equal side function notation usually starts with an f which stands for the name of the function (it can start with other letters too) and then it will have an input number in brackets beside it. On the right side of the equal side is the equation and wherever there’s an x is where you plug in the input number which should result in the answer of the question.