1. 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

2.  As a class, use your vast mathematical knowledge to define each of these words without the aid of your textbook. Rectangular Coordinates Cartesian Plane OriginQuadrants Ordered PairScatter Plot Pythagorean Theorem Midpoint SlopeLinear Equation

3. Cartesian Coordinate Plane The Cartesian Coordinate Plane is a flat place where points hang out  Usually called a “graph” ordered pairs  Uses ordered pairs of real numbers to locate points  Gives a visual representation of the relationship between x and y (Also called a Rectangular Coordinate System)

4.  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

5. Use your calculator to draw a scatter plot of the following data. Then find the line of best fit. x 012345678 y 1368457810

6. 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 1990475 1991577 1992521 1993569 1994609 1995562 1996707 1997723 1998718 1999648

7. 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.

8. If the coordinates of points A and B are ( x 1, y 1 ) and ( x 2, y 2 ), then

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

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

11. If A( x 1, y 1 ) and B( x 2, y 2 ) are points in a coordinate plane, then the midpoint M of AB has coordinates

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

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

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

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

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

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

18. linear function A linear function can have many forms, pick your favorite:  Slope-Intercept Form:  Point-Slope Form:  Standard Form:

19. 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.

20. Page 7 of your book contains these helpful formulas. Number them thusly: 1. 2. 3. 4. 5. 6. 7.8.9.

21. Given any of the previous formulas, what would it mean to solve for a particular variable? solve for a variable To solve for a variable in an equation or formula means to isolate that variable on only one side of the equation: variable = everything else

22. Solve V = (4/3)  r 3 for r.

23. 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