Linear Equations Mr. Abbott

Coordinate Plane In this unit we'll be learning about equations in two variables. A Coordinate Plane is an important tool for working with these equations. It is formed by a horizontal number line, called the x-axis, and a vertical number line, called the y-axis. The two axes intersect at a point, called the origin. You can locate any point on the coordinate plane by an ordered pair  of numbers (x,y), called the coordinates.

A Little Piece of History The idea of graphing with coordinate axes dates all the way back to Apollonius in the second century B.C. Rene Descartes, who lived in the 1600s, gets the credit for coming up with the two-axis system we use today. The story goes that he lay in bed and watched flies crawling over tiles on the ceiling. He realized that he could describe a fly's position using the intersecting lines of the tiles. The system is often called the "Cartesian coordinate system" in his honor.

Creating your own Coordinate Plane Start with a sheet of graph or grid paper. Next, draw a horizontal line. This line is called the x-axis and is used to locate values of x. To show that the axis actually goes on forever in both directions, use small arrowheads at each end of the line. Mark off a number line with zero in the center, positive numbers to the right, and negative numbers to the left.

Creating your own Coordinate Plane Next draw a vertical line that intersects the x axis at zero. This line is called the y-axis and is used to locate the values of y. Mark off a number line with zero in the center, positive numbers going upwards, and negative numbers going downwards. The point where the x and y axes intersect is called the origin. The origin is located at zero on the x axis and zero on the y axis.

Final Graph

Locating Points Using Ordered Pairs We can locate any point on the coordinate plane using an ordered pair of numbers like the example shown here, The ordered pair 4 and 2 (point P). We call the ordered pair the coordinates of the point. The coordinates of a point are called an ordered pair because the order of the two numbers is important.

Order Counts! The first number in the ordered pair is the x coordinate. It describes the number of units to the left or right of the origin. The second number in the ordered pair is the y coordinate. It describes the number of units above or below the origin.

Plotting Recap To plot a point, Start at the origin and count along the x axis until you reach the x coordinate, (count right for positive numbers, left for negative.) Then count up or down the number of the y coordinate (up for positive, down for negative.) Point is ( 5, 3)

Quadrants

Quadrants To make it easy to talk about where on the coordinate plane a point is, we divide the coordinate plane into four sections called quadrants. Points in Quadrant 1 have positive x and positive y coordinates.  Points in Quadrant 2 have negative x but positive y coordinates.  Points in Quadrant 3 have negative x and negative y coordinates.  Points in Quadrant 4 have positive x but negative y coordinates.

Write the letter of the point that matches each ordered pair

How to use data tables Pre- Algebra

What is a Data Table? A data table is a way to organize values of multiple relations. Data tables are used to compare sets of data with each other. Students Name Home Work turned in (out of 8) Grade on Test Student 1 1 30% Student 2 6 80% Student 3 7 85% Student 4 8 95% Student 5 3 60% Student 6 2 50% Student 7 90%

How do we use data tables? We turn data tables in graphs to give a better visual of what the data mean First we must decide what values of the data table we want to compare. Second I want to decide which value is the x and which is the y Then we will graph them as ordered pairs. Once graphed we must label our axis Title Students Name Home Work turned in (out of 8) Grade on Test Student 1 1 30% Student 2 6 80% Student 3 7 85% Student 4 8 95% Student 5 3 60% Student 6 2 50% Student 7 90%

Arm Length Vs. Height First we must decide what values of the data table we want to compare. Second I want to decide which value is the x and which is the y Find the range of each value. Then we will graph them as ordered pairs. Once graphed we must label our axis Title Student Arm length (in) Height (in) Student 1 50 48 Student 2 60 62 Student 3 65 Student 4 55 57 Student 5 45 Student 6 70 68 Student 7 40

Forearm length Vs. Hand Height You must collect data to fill in the data table below using a ruler After data table is complete create a graph by following the previous examples. Student Forearm Length (in) Hand Height (in) Student 1 Student 2 Student 3 Student 4 Student 5 Student 6 Student 7