Category: Math 10

This week in math 10 we learned about intro to systems solving using graphing

for this we would use the y=m+b equation, we will also have two of these,

for example

x- 4= y and y=3x-8

for this you want to start with what is easier, in this case it would be x-4=y, so what we would need to do is isolate x because it is already positive

so we add four on both side, the -4 and +4 cancel each other out so it is no longer there

x= y+4

 

now we have solved for x we have to solve for y, now we insert the x into wherever there is x in the other equation,

y=3(y+4)-8

from there we solve using BEDMAS

y=3y+12-8

from here we add like terms

-2y=4

now we divide everything by -2 to isolate the y which leaves us with

y=-2

from here we would put in y wherever y is to complete solving x

x- 4= -2

we need to isolate x so we add 4 on each side which leaves us with

x=-2+4

add like terms

x=2

now to verify we insert x and y into the original equations to see if we were correct

2-4=-2

the first one is true

-2=3(2)-8

-2=6-8

-2=-2

it is true for the second equation

 

 

This week in math 10 we learned about how to graph equations

I’m going to show how to graph using the slope and y-intercept

first have you equation, I’m going to use y=1x+2

when doing this you want to start on the y intercept like this

since we have our starting point now we can use the slope to find the rest of the line,

 

the slope is 1 which is also equal to 1/1 we are going up by 1 (rise) and to the right 1(run) because it is a positive, you keep going until you can no longer graph

from here to complete it go down 1 and to the left one to complete the line

 

at this point you would run a line through the points to connect them all (but straighter)

 

This week in math ten we learned about how to use two coordinates and turn them into a slope intercept equation, first you need to know what slope intercept looks like

(rise=y run=x)

this will be the example

(6,4), (8,5)

from there you would subtract the x’s with the second x first  and the y’s in with the second first

so it would look like this

from there you would subtract the numbers which leaves you with

now you have your slope, from here it gets easier

now you would put you slope where the rise over run is and your first set of coordinates into the second x and y

 

and that would be two sets of coordinates turned into a point slope equation which makes it easier to graph.

 

this week in math 10 we started a new unit on slope and linear functions.  i will be showing how to find the slope on a graph.

first you need to know the slope formula

slope= rise/run

rise=y

run= x

so above is the formula on how to find the slope

the reason why y=rise and x=run  is because when were looking at it on a graph we would go up or down on y or the top number and to the sides on x or the bottom number.

 

this is what i will be using as an example

to find the rise you would see how many squares/numbers you need to go up to reach the line

and because this slope is going up it will be positive.

the rise would be one because it only took one to line up with the slope.

now we have our rise we need to figure out our run

to do this we need to figure our how many points it takes to reach the line/slope

for this one it would take 2

now we have our rise and run.

rise=1

run=2

from there we would turn it into a fraction

1/2 would be the slope on this graph, to check if it’s right try using it again until you reach the top.

 

 

 

 

This week in math 10 we learned about Function Notation, one part of this is on a graph and seeing if it can pass the vertical line test. Basically the vertical line test is to see if it is a function or not a function, to do this you would look at a graph and see if any of the vertical lines/ the y-axis has two points or if it only has one for each x-axis

for example

this graph would be a function because it passes the vertical line test, it doesn’t have more the one point on the y-axis

another example

this one would not be a function because there a two y-axis points for a x-axis

last example

this one looks a little confusing but looking at it, this one is also a function because it still only has one point per x-axis

This week in math 10 we learned how to find the domain and range. I will be showing how to find the domain.

first the definitions

the domain is the set of all input values that can be used for a relations,

the range is the set of all output values that are used by a relation.

when finding the domain or range we would use a graph

this is what I’m going to be solving

to find the domain i first need to see where the dots would land on the horizontal line or x which would be -4 and +6

from here I would make the equation, the equation should look like this

a ≤ x ≤ b

the greater than/ equal to signs would go in the direction of the greater number so our equations would look like

-4 ≤ x ≤ 6

something to remember is when the dot is closed it would be the greater than sign with the line meaning it could be equal to and when the dot is open it would just be the greater than sign.