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Contents

## Summary

We have learned a lot of new material recently. We talked about linear equations. We talked about inequalities and absolute value. Now let's review.

## Point Slope

One useful way to represent a line is using the point slope form. If we know the slope of a line, and a single point that the line goes through, we can use this formula to express the equation of a line. Let's say you have a line that goes through the point 4, 7 with slope of negative 3. What is the equation of that line?

## Point Slope

Well, the point slope formula takes a point written as x1y1 and a slope m. The equation is then, y minus y1 equals m times the quantity x minus x1. In this situation our point is 4,7 and m is negative 3. So the answer is y minus 7 equals negative 3 times the quantity x minus 4.

## Factoring

We also learned how to simplify equations by pulling out a common factor. Can you factor out the common term in this expression?

## Factoring

The 8 and 12 share 4 as a common factor. They each share an x and a y as well. So the factored version of this would be, 4xy times the quantity 2x plus 3y.

## Absolute Value

We learned that absolute value really represents the difference between two numbers. How would you write the following sentence as an absolute value equation? The distance between x and 8 is less than 3.

## Absolute Value

The distance between x and 8 is represented as the absolute value of x minus 8. Since that must be less than 3, the solution is absolute value of x minus 8 is less than 3.

## Interval Notation

Looking at this statement, the absolute value of x minus 8 is less than 3. How would you write the solution to this inequality using interval notation?

## Interval Notation

We can write negative 3 as less than x minus 8 which is less than 3. Adding 8 gives us 5 is less than x, which is less than 11.

## Solve

We also saw that some equations which don't initially look linear actually are. Can you solve the following equation for x?

## Solve

Noting that x cannot equal negative 4 and x can also not equal 0, since that would make the denominator 0. Multiply both sides by the denominators, the quantity 4 plus x and 2x, not forgetting the parentheses. Distribute. Subtract divide by negative 27. And the answer is 4 over 27.