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Saturday 13th of July
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Power of a Quotient Property of Exponents
Adding and Subtracting Fractions
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The Quadratic Formula
Fractions and Mixed Numbers
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Polar Form of a Complex Number
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Common Logs
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Higher Degrees and Variable Exponents
Solving Quadratic Inequalities with a Sign Graph
Writing a Rational Expression in Lowest Terms
Solving Quadratic Inequalities with a Sign Graph
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The Square of a Binomial
Properties of Negative Exponents
Inverse Functions
Rotating an Ellipse
Multiplying Numbers
Linear Equations
Solving Equations with One Log Term
Combining Operations
The Ellipse
Straight Lines
Graphing Inequalities in Two Variables
Solving Trigonometric Equations
Adding and Subtracting Fractions
Simple Trinomials as Products of Binomials
Ratios and Proportions
Solving Equations
Multiplying and Dividing Fractions 2
Rational Numbers
Difference of Two Squares
Factoring Polynomials by Grouping
Solving Equations That Contain Rational Expressions
Solving Quadratic Equations
Dividing and Subtracting Rational Expressions
Square Roots and Real Numbers
Order of Operations
Solving Nonlinear Equations by Substitution
The Distance and Midpoint Formulas
Linear Equations
Graphing Using x- and y- Intercepts
Properties of Exponents
Solving Quadratic Equations
Solving One-Step Equations Using Algebra
Relatively Prime Numbers
Solving a Quadratic Inequality with Two Solutions
Operations on Radicals
Factoring a Difference of Two Squares
Straight Lines
Solving Quadratic Equations by Factoring
Graphing Logarithmic Functions
Simplifying Expressions Involving Variables
Adding Integers
Factoring Completely General Quadratic Trinomials
Using Patterns to Multiply Two Binomials
Adding and Subtracting Rational Expressions With Unlike Denominators
Rational Exponents
Horizontal and Vertical Lines
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Straight Lines

A. Necessary Concepts, Forms of the Equation, and Formulas:

1. The slope of a line is the tilt or slant.


3. Standard form for the equation of a line is:

Ax + By = C (notice this is just the x term first, then the y term, then the equals sign, and finally the constant)

Example: 3x - 5y = 7

4. The equation of a line may also be written in slope-intercept form:

y = mx + b (notice this equation is solved for y)

Example: y = -2x + 4

5. Lines with a positive slope rise from lower left to upper right.

Lines with a negative slope fall from upper left to lower right.

6. Two lines are special:

Vertical Lines have the form x = a and have no slope number.

Horizontal Lines have the form y = b and a slope of zero.

Example: x = 5 will be vertical and have no slope.

Example: y = -3 will be horizontal and have a slope of zero.

7. The point-slope form of the equation is most often used to find the equation of a given line:

y - y 1 = m (x - x 1)

If you know one point and the slope, use the point slope form to determine the equation of the line.

8. Parallel lines have the same slope (they are slanted the same).

Perpendicular lines have slopes that are negative reciprocals of each other. This means the slopes must meet two conditions: opposite in sign and "flipped".

Following are the things you should be able to do concerning the straight line: B. Find the slope, given:

1. the graph

Choose two definite points the line passes through. In our example, they are heavy dots.

Note the directions you must travel to move from one point to the other. Let's move from the top left one to the lower right.

We would have to move down 2, then right 3. This represents a change in y of -2 (down) and a change in x of +3 (right). Therefore, the slope is , or just .

2. two points Example:

given (-2,3) and (4,7), just apply the formula for the slope:

Look at the two points in this way:

x 1 ,y 1   x 2 ,y 2
(-2, 3) and (4, 7)

and apply the formula for the slope.

3. the equation in slope-intercept form If the equation is given to you in slope-intercept form, you're in luck! You can read the slope directly from the equation. Example:given y = 3 x - 7, note how this fits slope-intercept form shown below: y = m x + b Therefore, the slope is 3.

4. the equation in standard form: Ax + By = C

The slope will be .

Example: Given the equation of a line to be 3x - 6y = 7, the slope will be


C. Find the equation, given:

1. One point and the slope.

Use the point-slope form of the equation!

Example: Given that a line has slope of -3 and passes through (-4,5), find the equation.

Substituting into the point-slope form gives us:

y - 5 = -3[x - (-4)]

y - 5 = -3[x + 4]

y - 5 = -3x - 12

At this point, we can put the equation in either standard form or slope-intercept form.

In standard form we would have 3x + y = -7

In slope-intercept form we would have y = -3x - 7

2. Two points.

Use the slope formula to find the slope, then use this slope with either of the two points in the point-slope form of the equation as shown above.

3. The slope and the y-intercept.

Simply substitute both into the slope-intercept form of the equation.

Example: Given the slope of a line is 2/3 and the y-intercept is -4, find the equation.

Since m = 2/3 and b = -4, we may substitute into y = mx + b

4. Given x- and y-intercepts.

If the x-intercept is -3 and the y-intercept is 7, remember the actual coordinates of these points are then (-3,0) and (0,7). What you have really been given are two points so work the problem as in #2 above.

D. Graphing the equation, given:

1. The slope and the y-intercept.

Follow these two steps:

a. plot the point which is the y-intercept

b. use the slope as directions to a new point

Example: Graph the line with the slope of -3 and y-intercept of 2.

The line can now be drawn connecting the two points.

2. Given one point and the slope of a line.

Use the same procedure as above. Plot the given point, then use the slope as directions to a new point.

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