This week we learned about the different equations to make the equations of the line.
The most important thing to find is the slope(rise/run). Which we can figure out with 2 clues(x,y).
Slope y- intercept form: y=mx+b
Point- slope form: m(x-x)=y-y
General form(pretty form): ax+by+c=0
-A,B,C all have to be integers.
– To get to general form you first have to get it to slope y intercept form or point slope form.
On the 15th week we learned more about slopes.
Colinear: points lining up
Parallel lines: lines that never cross and have the same slope. Ex) m1= m2
Perpendicular lines: two lines that meet at 90 degrees. Ex) m1= 3/4, m2= -4/3
We also started to learn about how to incorporate the last unit domain and range to this unit.
Ex) In a linear equation the amount that y1 to y2 increases or decreases by would be the slope(6) multiplied x. When you multiply the slope(6) to the input(1) you should get the output(2). If it isn’t equivalent then the number that would be added or taken away to get the output, which in this case -4 would be the y-intercept.
Blue- Point-slope form
Yellow- Slope Y intercept form
Purple- horizontal and vertical line
This week in math we started a new unit on slopes.
We learned that a slope is a number that describes the steepness of a line, which is the same as the tangent ratio(trigonometry).
slope= rise(y)/ run(x)
Positive slope: The slope rises from left to right
Negative Slope: The slope decreases from left to right
This week in math we learned more about relations and functions. We reviewed how to write out inequalities and we also learned about domain and range. At first I was confused about the whole concept of the input and outputs but once I got used to solving more equations it got easier to do.
Domain: the independent(input) variable in the relation.
Range: the set of all numbers for the dependent(output) variable in the relation.
Function: a special realtion where every input(x) has only one output(y).
To evaluate a function you would have to substitute the variable with the given number which in this case would be 5 and -8. To solve the equation remember to always use B.E.D.M.A.S!!
This week in math we started to learn about relations and functions. We reviewed linear relations from grade 9. And we learned how to find the intercepts of x and y on a graph.
To find the the x intercept you would multiply the y to 0. Then you would single out the x by deviding both sides by 4.
To find the y intercept you would multiply x by 0, and devide both sides by 7 to single out the y.
With the two answers you are now ready to draw the graph.
On week 11 of math we reviewed all the units for our mid terms. One thing I forgot and had to review was how to catagorize numbers into groups from chapter 1.
R stands for real numbers which are all numbers including rational and irration numbers.
The Q with the line on too of it stands for irrational numbers which are also known as “ugly numbers”. They are numbers that cannot be written as a fraction.
Q stands for rational numbers. They are all the numbers that can be written as a fraction.
I stands for integers. They are all positive(whole) numbers including negative numbers.
W stands for whole numbers. Which are all positive natural numbers including 0.
N stands for natural numbers. They are all the positive numbers.
This week of math we learned how to factor trinomials.
Example 2) Find the possible 2 integers that equal to 24 when multiplied together. Pick the pair of integers that equal to 11 when added together. Make sure to see if the integers have to be possitive or negative depending on the middle and last number (11, 24). If there is no pair that equals to the middle number when added together, it can’t be factored. The integers can be written in any
The is week in math we learned how to remove the greatest common factor. This helps factoring easier.
1. Factor all three numbers.
2. Take the common numbers and write it in front of the brackets.
3. Divide the three numbers by the common number and write it inside the brackets.
Example 1) In the first example you can see that 10, 25, and 30 can all be divided by 5 and X. So i wrote 5X infront of the brackets and then divide 10, 25, and 30 by 5, and you’ll eventually end up with 2, 5, and 6, which you write in the brackets, and also don’t forget to subtract the common X from each number.