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.
This week I learned about functions. I didn’t know about functions before and how we’re able to tell if something is a function or not. A function is a “special relation” It’s when the y value/output only has one x value/input. This means if you graphed the points on a graph, there wouldn’t be a dot over top another. One test to see if a relation is a function on a graph is the vertical line test which means, if you look across the vertical line (x axis) there should NOT be one dot over another.
This week we talked more midterm review. I went over stuff from the beginning of math like number and exponents, and now I understand the concepts way more than before. I’m glad we got class time and review papers because it helps refresh the memory. One thing I had to make sure of was negative exponents which I almost forgot how to do, even though it wasn’t that long ago. I practiced on reciprocating then equation before solving it so it would make the question much easier.
This week I learned more about the vocabulary for linear relations. For example,
Discrete variables= no connecting dots on a x, y axis. Counting numbers (1, 2, 3).
Continuous variables= connect the dots, used to measure. (1.5, 2.5, 3.5)
Domain/input/independent variable= x
Range/output/dependent variable= y
Ordered pairs= x, y
This week I learned how to factor binomials and trinomials. If you’re given a polynomial equation that has alreasy been answered fully, then you’ll be able to factor based on the criteria.
If it’s a binomial (2 terms) the sign has to be negative
In a trinomial, focusing on the first term and the last is important, if in correct order= x2 + x + 1