This week in math we learned how to solve word problems. First, you find the variables which represent unknown values. Second, you form a system of equations that involve the variables. Third, you solve the system. Finally, you can answer the problem and verify the solution. When there are word problems that introduce the distance, speed, or time of something, you can use the formula speed multiplied by time equals distance. (TxS=D)

http://www.scruffs.shetland.co.uk/files/dst.htm

https://en.wikipedia.org/wiki/System_of_linear_equations

This week in math we learned about systems of linear equations. They are a set of two linear equations with two variables. The two ways we learned to solve them are by substitution and elimination. For the substitution method, you try and isolate a variable by moving it to one side and having the rest of the equation on the other. You then can put your equation into the other by inserting the variable you have isolated with the other side of the equation. From there you solve the equation until you get a variable = a number.

The other method is elimination. For this method, you have to find or create a zero pair with one of the variables by multiplying or dividing the entire equation. Once you have a zero pair, you can subtract one equation from another to have a single equation. Finally, you simplify the equation until you get a variable = a number

https://en.wikipedia.org/wiki/System_of_linear_equations

This week in math we learned about the 3 different types of slope formulas.

Y-intercept: Mx+B=Y

Point Slope: Y-y = M(X-x)

General Form: ax+bx+c=0

You can convert every slope into another by simply using algebra. First, you need to find the slope using the difference of y over the difference of x. From there, you can turn the slope into a Point Slope equation by inputting the coordinates into the formula. You can also then take those numbers and convert them into the Y-intercept. Finally, you can turn it into a general equation by using algebra to move everything to one side.

This week in math we learned about calculating the slope formula of 2 coordinates. The formula is m (Subscript) ab = y(subscript)b- y(Subscript)a over x(Subscript)b – x(Subscript)a. This means you take the A & B coordinates, subtract the “y” A coordinates from the B coordinates, and divide that by the x a minus b coordinates.

(I’m not sure if I did this right)

This week in math we learned how to find ” F(x)” using a formula.

In this first question, you are trying to find “X”. Since “f(X)” = 43, you can write the equation: (43=5x-7). Then you can just use algebra to find what “X” is.

This week in math we learned about the domain and range in a graph. When you are asked to find the domain, you need to find to which numbers “X” could possibly be. When asked to find the range, you find “Y”. To start, you first need to look at the lowest point and see if the dot is filled in. If it is, your sign will be < with a line underneath which means “X” is equal to or greater than that number. If the dot isn’t filled in, “X” will be greater than the number. You then find the highest point and do the same thing. Your equation should look like this:

This week we mostly studied for the mid-term. One thing I did learn was how exponents on negative numbers work with brackets and no brackets. If there are no brackets on the negative number, the exponent only multiplies by the number, making the final answer a negative no matter what. If brackets are on the number, you have the whole number to multiply. If the exponent is an even number, the answer will be positive. If the number is odd, then the answer will be negative.

This week we learned about multiplying trinomials. When multiplying trinomials, you take your first number and multiply it to every number on the other side. Finally, you simplify the question by combining like terms until you end up with your answer.

We also learned that if there is an exponent on the outside of the bracket, you have to multiply the entire bracket by another of the same entire bracket.