We will assign a number to a line, which we call slope, that will give us a measure of the "steepness" or "direction" of the line. It is often convenient to use a special notation to distinguish between the rectan- gular coordinates of two different points.

But word problems do not have to be the worst part of a math class. By setting up a system and following it, you can be successful with word problems. So what should you do? Here are some recommended steps: Read the problem carefully and figure out what it is asking you to find.

Usually, but not always, you can find this information at the end of the problem. Assign a variable to the quantity you are trying to find. Most people choose to use x, but feel free to use any variable you like. For example, if you are being asked to find a number, some students like to use the variable n.

It is your choice. Write down what the variable represents. At the time you decide what the variable will represent, you may think there is no need to write that down in words.

However, by the time you read the problem several more times and solve the equation, it is easy to forget where you started. Re-read the problem and write an equation for the quantities given in the problem. This is where most students feel they have the most trouble.

The only way to truly master this step is through lots of practice. Be prepared to do a lot of problems. The examples done in this lesson will be linear equations.

Solutions will be shown, but may not be as detailed as you would like. If you need to see additional examples of linear equations worked out completely, click here. Just because you found an answer to your equation does not necessarily mean you are finished with the problem.

Many times you will need to take the answer you get from the equation and use it in some other way to answer the question originally given in the problem. Your answer should not only make sense logically, but it should also make the equation true.

If you are asked how fast a person is running and give an answer of miles per hour, again you should be worried that there is an error. If you substitute these unreasonable answers into the equation you used in step 4 and it makes the equation true, then you should re-think the validity of your equation.

When 6 is added to four times a number, the result is What are we trying to find? Assign a variable for the number. We are told 6 is added to 4 times a number. Since n represents the number, four times the number would be 4n.

If 6 is added to that, we get. We know that answer is 50, so now we have an equation Step 5: Answer the question in the problem The problem asks us to find a number. The number we are looking for is The answer makes sense and checks in our equation from Step 4. The sum of a number and 9 is multiplied by -2 and the answer is We are then told to multiply that by -2, so we have.

Be very careful with your parentheses here. The way this is worded indicates that we find the sum first and then multiply.kcc1 Count to by ones and by tens.

kcc2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1). kcc3 Write numbers from 0 to Represent a number of objects with a written numeral (with 0 representing a count of no objects).

kcc4a When counting objects, say the number names in the standard order, pairing each object with one and only. kcc1 Count to by ones and by tens.

kcc2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1). kcc3 Write numbers from 0 to Represent a number of objects with a written numeral (with 0 representing a count of no objects).

kcc4a When counting objects, say the number names in the standard order, pairing each object with one and only. As you can see the solution to the system is the coordinates of the point where the two lines intersect. So, when solving linear systems with two variables we .

Section Solving Exponential Equations. Now that we’ve seen the definitions of exponential and logarithm functions we need to start thinking about how to solve equations involving them.

After completing this tutorial, you should be able to: Know if an ordered pair is a solution to a system of linear equations in two variables or not. (Note that with non-linear equations, there will most likely be more than one intersection; an example of how to get more than one solution via the Graphing Calculator can be found in the Exponents and Radicals in Algebra section.) Solving Systems with Substitution.

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Recurrence relation - Wikipedia