Amanda K's Page

Amanda's Tip's for
Equations

Do you feel like you have gotton off track when you're in
Algebra Class!?!
Then maybe you should to take a look at this!!!

Literal Equations

Solve for d₁

1/2 (d₁₊d₂)=A+BT The original equation is known as Caillete's and Mathia's Law.

d₁+d₂=A+BT
             1/2 The first step is to divide by 1/2 to get rid of the fraction. When you do this then you have to divide by the other side which means that you would technically be dividing A+BT by 1/2.

d₁= A+BT_-d2
^1/2 You now are trying to get the d₁by itself so you have to subtract the d₂from both sides of the equation.

d₁=A+BT_-d2
       1/2 This is the final equation for the equation known as Caillete's and Mathia's Law.

Helpful ways to Solve Equations

-By adding, subtracting, multiplying, or dividing by any single value ot parenthesis value
-Using the distributive property or factor as needed
-Square root or square the variables
-Get rid of any root or power
-Use substitution

Linear Equation

t=2-2[2t-3(1-t)] This is the original equation, you need to solve for t.

t=t-2[2t-3+3t] The first step is to get rid of the parenthesis. To do this you have to use the distributive property. You are going to have to distribute the 3(1-t).

t=2-2(5t-3) You now can now add the like terms that are inside the parenthesis.

t=2-10+^-6 Now distribute the 2(5t-3).

t=8-10t You can add like terms again.

11t=8 To find out what t equals you have to divide by 11 on both sides. You are now at the point were you have the t on one side of the = sign and the number on the other. The purpose of this problem was to find t so you have to divide by 11 to get the t by itself.

t=.73 Once you divide by both sides you final answer will appear.

3 Ways to find the slope of a Line
-point slope y₂-y₁=m(x₂-x₁)
-slope intercept y=mx+b
-standard form ax+by=c

*All of these equations mean the same thing, each one is just another way to write it. When you are having to write all of the different methods like point slope, slope intercept, and standard form they all work together.   What I mean is when you find the answer to one equation you can use that information and plug it into the next one.

Point Slope

y₂-y₁=m(x₂-x₁)
slope=3 y intercept=(2,9)

y-9=³/₁(x-2) This is your final answer. All you have to do to solve for these types of equations is to stick in all of the known variables. In the parenthesis the 2 is the x variable and the 9 is your y. The letter m represents the slope so 3 is equal to the slope. So you simply replace them with the letter that they represent.

Slope Intercept
y=mx+b
slope=3 y intercept (2,9)

9=3(2)+b The first step is to try to solve for b. The first thing that you have to do is plug all of the known variables into the equation

9 = 6 =b
-6 -6 3=b Once your letters are replaced by numbers you simply solve the equation. Since you are trying to get the b by itself you have subtract 3 from both sides. You then find out that b=3.

y=3x+3 To find the final answer you plug in the slope which is 3x and then you replace the b with the number that you solved for.

Standard Form
ax+by=c
slope 3    y intercept (2,9)

-3x-y=3 Since you have already found the answer for slope intercept, you simply rearrange the numbers to make them fit into the standard form equation.

3x-y=^-3 Once you have rearranged you numbers you will have encountered negatives and sometimes even fractions. When this occurs make sure that the x variable doesn't have a negative, decimal or fraction.

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1/2 (d₁₊d₂)=A+BT	The original equation is known as Caillete's and Mathia's Law.
d₁+d₂=A+BT 1/2	The first step is to divide by 1/2 to get rid of the fraction. When you do this then you have to divide by the other side which means that you would technically be dividing A+BT by 1/2.
d₁= A+BT_-d2 ^1/2	You now are trying to get the d₁by itself so you have to subtract the d₂from both sides of the equation.
d₁=A+BT_-d2 1/2	This is the final equation for the equation known as Caillete's and Mathia's Law.

t=2-2[2t-3(1-t)]	This is the original equation, you need to solve for t.
t=t-2[2t-3+3t]	The first step is to get rid of the parenthesis. To do this you have to use the distributive property. You are going to have to distribute the 3(1-t).
t=2-2(5t-3)	You now can now add the like terms that are inside the parenthesis.
t=2-10+^-6	Now distribute the 2(5t-3).
t=8-10t	You can add like terms again.
11t=8	To find out what t equals you have to divide by 11 on both sides. You are now at the point were you have the t on one side of the = sign and the number on the other. The purpose of this problem was to find t so you have to divide by 11 to get the t by itself.
t=.73	Once you divide by both sides you final answer will appear.

9=3(2)+b	The first step is to try to solve for b. The first thing that you have to do is plug all of the known variables into the equation
9 = 6 =b -6 -6 3=b	Once your letters are replaced by numbers you simply solve the equation. Since you are trying to get the b by itself you have subtract 3 from both sides. You then find out that b=3.
y=3x+3	To find the final answer you plug in the slope which is 3x and then you replace the b with the number that you solved for.

-3x-y=3	Since you have already found the answer for slope intercept, you simply rearrange the numbers to make them fit into the standard form equation.
3x-y=^-3	Once you have rearranged you numbers you will have encountered negatives and sometimes even fractions. When this occurs make sure that the x variable doesn't have a negative, decimal or fraction.