objectives: 1.to do all kinds of things with points in the cartesian plane: scatter plot, distance,...
TRANSCRIPT
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
To the nearest hundredth of a unit, what is the approximate length of RS, with endpoints R(3, 1) and S(-1, -5)?
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
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 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.
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