Analytic Geometry Review

The Plane

Horizontal Axis: X Vertical Axis: Y The intersection is called the origin (0,0) All ordered pairs are given as (X,Y)

To plot the point (3,2)

X Y (3,2)

Plot the point (4,-3)

X Y (4,-3)

To plot the point (-3, 1)

X Y (-3,1)

BATTLESHIP

You get 5 boats 3 dots long 4 dots long 5 dots long 6 dots long 7 dots long

3 dot ship 4 dot ship Call (3,5) Miss!!! Call (4,9) HIT!!

Consider the linear relationship of getting paid $7.00 / hour This relationship can be expressed in 3 ways: 1. A table of values 2. A graph 3. An equation

Generate a table of values PT Make a graph: (3,21) (2,14) (0,0) (1,7) T P Equation: P = 7T (Y = 7X) 7 1 FD Slope = run = 7 1 rise

Suppose you get paid $20.00 for just showing up (gas?…)

Generate a table of values PT Use the same graph T P Equation: P = 7T + 20 (Y = 7X + 20) (0,20) (1,27) (2,34)

For the equation y = mx + b Algebraically m : the rate of change b : the initial value Graphically m : the slope b : the y-intercept (where the line crosses the y axis)

y = mx + b slope y- intercept

For example: It cost $ to rent a studio plus $5.00 to make each CD. Write the equation: C = 5d

For example: It cost $ to rent a hall plus $5.00 per person to attend. Write the equation: C = 5d

For example: It is 20 degrees at noon, and the temperature drops 2 degrees every hour. Write the equation: T = – 2h + 20

The equation of a straight line can be represented by the equation y = mx + b It can also be written as Ax + By + C = 0

To graph a line in this form, find the x and y intercepts. Ex. Graph 4x + 3y + 12 = 0 x y 0 4(0) + 3y + 12 = 0 3y + 12 = 0 3y = -12 y = -4 -4

To graph a line in this form, find the x and y intercepts. Ex. Graph 4x + 3y + 12 = 0 x y 0 4x + 3(0) + 12 = 0 4x + 12 = 0 4x = -12 x =

Graph a line passing through the points (0,4), (-3,0) X Y (0,-4) (-3,0)

Pg 4 1,2 Pg 5 1,2, then 1