Objectives:1. To do all kinds of

things with points in the Cartesian plane: scatter plot, distance, midpoint, slope, equation

2. To solve an equation for a particular variable

As a class, use your vast mathematical knowledge to define each of these words without the aid of your textbook.

Rectangular Coordinates Cartesian Plane

Origin Quadrants

Ordered Pair Scatter Plot

Pythagorean Theorem Midpoint

Slope Linear Equation

The Cartesian Coordinate Cartesian Coordinate PlanePlane is a flat place where points hang out

Usually called a “graph” Uses ordered pairsordered pairs of real

numbers to locate points Gives a visual

representation of the relationship between x and y (Also called a Rectangular Coordinate System)

1596-1650 French philosopher-etc. Cogito Ergo Sum A fly taught him about

the Cartesian coordinate plane and analytic geometry, for which he took full credit

Use your calculator to draw a scatter plot of the following data. Then find the line of best fit.

x 0 1 2 3 4 5 6 7 8

y 1 3 6 8 4 5 7 8 10

From 1990 through 2003, the amounts A (in millions of dollars) spent on skiing equipment in the United States are shown in the table, where t represents the year. Sketch a scatter plot of the data.

Year, t Amount, A

1990 475

1991 577

1992 521

1993 569

1994 609

1995 562

1996 707

1997 723

1998 718

1999 648

In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

c 2

b 2

a 2

If the coordinates of points A and B are (x1, y1) and (x2, y2), then

2122

12 yyxxAB

To the nearest hundredth of a unit, what is the approximate length of RS, with endpoints R(3, 1) and S(-1, -5)?

The distance between (-4, k) and (4,4) is 10 units. Find the value of k.

If A(x1,y1) and B(x2,y2) are points in a coordinate plane, then the midpoint M of AB has coordinates

2

,2

2121 yyxx

Find the midpoint of the segment with endpoints at (-1, 5) and (3, 3).

The midpoint C of IN has coordinates (4, -3). Find the coordinates of point I if point N is at (10, 2).

Slope can be used to represent an average rate average rate of changeof change.

A rate of change is how much one quantity changes (on average) relative to another.

For slope, we measure how y changes relative to x.

The slopeslope m of a nonvertical line is the ratio of vertical change (the rise) to the horizontal change (the run).

Find the slope of the line passing through the points (-4, -5) and (6, -2).

Find the value of k such that the line passing through the points (-4, 2k) and (k, -5) has slope -1.

A linear function linear function can have many forms, pick your favorite:

Slope-Intercept Form:

Point-Slope Form:

Standard Form:

y mx b

Ax By C

1 1y y m x x

Write the equation of the line through the points (-2, 5) and (4, -7). Write your answer in point-slope, slope-intercept, and standard forms.

Page 7 of your book contains these helpful formulas. Number them thusly:

1.2.

3.4.

5.6.

7. 8. 9.

Given any of the previous formulas, what would it mean to solve for a particular variable?

To solve for a variablesolve for a variable in an equation or formula means to isolate that variable on only one side of the equation:

variable = everything else

Solve V = (4/3)r3 for r.

Objectives:1. To do all kinds of

things with points in the Cartesian plane: scatter plot, distance, midpoint, slope, equation

2. To solve an equation for a particular variable