Chapter P Review

 

The Cartesian Plane: Formed by using two real number lines intersecting at right angles

 

 

 

Each point in the plane corresponds to an ordered pair (x,y)

 

The Distance Formula:

 

 

 

The Midpoint Formula:

 

 

 

 

 

The Equation of a Circle (standard form):

 

  

 

 

How to Sketch the Graph of an Equation:

1. Rewrite the equation so that one of the variables is isolated on one side of the equation.

2. Make a table of several solution points.

3. Plot these points in the coordinate plane.

4. Connect the points with a smooth curve.

 

Slope:

 

Point-Slope Form:

 

 

Find an equation of the line that passes through the point (1,-2) and has a slope of 3.

 

 

 

 

Points of Intersection:

Find the points of intersection of the graphs of   and

To begin, solve each equation for y:

  and  

Next, set the two expressions equal to each other:

 

Multiply each side by 3:

 

Subtract 12x and 2 from each side:

 

 

When x=2, the y-value of each of the given equations is 2. So, the point of intersection is (2,2)

 

Inequalities:

1. Transitive Property

a < b and b < c = a < c

 

2. Addition of Inequalities

a < b and c < d = a + c < b + d

 

3. Addition of a Constant

a < b = a + c < b + c

 

4. Multiplying by a Constant

For c > 0, a < b = ac < bc

For c < 0, a < b = ac > bc

 

Solve. Express your solution in interval notation.

 

Multiply both sides by 3

 

Subtract both sides by -1

 

Divide each side by 4

 

Interval Notation