Courtney's Algebra Web Page

This web page is going to show you how to solve linear equations, solve literal equations, and how to find the equation of a line in three different forms.

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Solving Linear Equations

   ~ A linear equation in one variable is an equation that can be written in the form of ax=b.  The a and the b would be the constants, and a cannot equal zero.  Linear equations have one variable.
5x+11=7x-9
This is the linear equation.
5x+20=7x
We added 9 to both sides to get rid of the -9.
20=2x
To get the variables on 1 side we subtracted 5x from both sides.
10=x
We divided by 2 on both sides in order to get the variable by itself.

** You must remember that what you do to one side of the equation you must do to the other side.


4(3x-5)= -2(-x+8)-6x
This is a tougher linear equation.
12x-20=2x-16-6x
In this step we used the distributive property to get rid of the parentheses.
12x--20= -4x-16
Now we combined like terms on both sides.
16x-20= -16
We added 4x to both sides to get the variables on one side of the equation.
16x=4
Next, we added 20 to both sides to get rid of the -20.
x=(1/4)
To get the variable by itself, we divided 4 by 16. 

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Solving Literal Equations

~ Literal equations have more than one variable.  These equations are solved for a specific variable in terms of the other variables.  You can't have a numerical answer for this type of equation.  Literal equations can also be called formulas.  You will have the answer to your equation once you have the variable that you are solving for by itself on one side the equation.

* In this example solve for y *
7x-3y =8
This is the literal equation.
-3y = 8-7x
In this step, we subtracted 7x from both sides.
y = (-7x + 8) / -3
Next, we divided the both sides by -3, to get y by itself.
y = (-7x/-3) + (8/-3) 
Now, we divided the 7x and the 8 by -3.
y = (7/3)x + (-8/3)
This is the answer when you solve for x.
** Remember, what you do to one side of the equation you must also do to the other side**

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Finding the Equation of a Line

~ There are three different ways to find the equation of a line.  The three ways are: slope intercept form, using two points, and point slope form.

Slope Intercept Form

~ Slope intercept form is used when you are given the slope m and the y-intercept b to form the equation y = mx+b.  All you have to do once you have the slope and the y-intercept is plug them into the equation.

Example:    m = 5    b = -3
The answer is: y = 5x - 3.

Example #2:    m = -(3/4)    b = (7/3)
The answer is: y = -(3/4)x + (7/3)

Point Slope Form

~ Point slope form is used when you are given the slope m and a point (x1, y1 ), use the equation y-y1 = m(x-x 1).  All you have to do to solve this problem is plug in the slope and the point, and then solve for y.
Example:    m = (3/2)    point: (0 , 1)

Step 1:  y-y1 = m(x-x 1)

Step 2:  y-(-1) = (3/2)(x-0)

Step 3:  y + 1= (3/2)x

Step 4 (answer): y = (3/2)x - 1
 

Two Points

~ When you are given two points (x1, y1 ) and (x2, y2) you would use the formula  m = (y2-y1 /x2-x1) to find the slope of the line.  Next, you would use the point slope form using the slope and one of the points that were given to write the equation for the line.

Example:  points: (-2, -1) and (3, 4)
Step 1:    m = (y2-y1/x2-x1)
 Step 2:   m = (4- [-1]/3- [-2])
Step 3:    m = (5/5) = 1
** Now we know that the slope is 1**
Step 4:    y-y1 = m(x-x1)
Step 5:    y-(-1) = 1(x-[-2])
Step 6:    y + 1 = x + 2
Step 7 (answer):    y = x + 1

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Links 

 ~ Visit other student's Algebra pages

~ Visit Union Grove High School's web page



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