We can label these points on the grid as in Figure 15.įor the following exercises, use your graphing calculator to input the linear graphs in the Y= graph menu.Īfter graphing it, use the 2 nd CALC button and 2:zero button, hit ENTER.
![coordinate graphs coordinate graphs](https://printablee.com/postpic/2014/12/printable-coordinate-graph-paper_333910.png)
Lastly, she traveled 4 blocks north to ( 8, 7 ). After that, she traveled 3 blocks east and 2 blocks north to ( 8, 3 ). The next stop is 5 blocks to the east, so it is at ( 5, 1 ). For example, the first stop is 1 block east and 1 block north, so it is at ( 1, 1 ). If we set the starting position at the origin, we can identify each of the other points by counting units east (right) and north (up) on the grid. The first thing we should do is identify ordered pairs to describe each position. Compare this with the distance between her starting and final positions. Find the total distance that Tracie traveled. Each stop is indicated by a red dot in Figure 1. On the way, she made a few stops to do errands. Tracie set out from Elmhurst, IL, to go to Franklin Park. Let’s return to the situation introduced at the beginning of this section. Notice that the graph crosses the axes where we predicted it would.įinding the Distance between Two Locations We can confirm that our results make sense by observing a graph of the equation as in Figure 11. For example, lets find the intercepts of the equation y = 3 x − 1. Similarly, to determine the y-intercept, we set x equal to zero and solve for y. To determine the x-intercept, we set y equal to zero and solve for x. The y-intercept is the point at which the graph crosses the y-axis. The x-intercept is the point at which the graph crosses the x-axis. The intercepts of a graph are points at which the graph crosses the axes. Each section is called a quadrant the quadrants are numbered counterclockwise as shown in Figure 2 Perpendicular to each other, the axes divide the plane into four sections. The Cartesian coordinate system, also called the rectangular coordinate system, is based on a two-dimensional plane consisting of the x-axis and the y-axis. Descartes named the horizontal axis the x-axis and the vertical axis the y-axis. While there is evidence that ideas similar to Descartes’ grid system existed centuries earlier, it was Descartes who introduced the components that comprise the Cartesian coordinate system, a grid system having perpendicular axes. Further, by dividing each axis into equal unit lengths, Descartes saw that it was possible to locate any object in a two-dimensional plane using just two numbers-the displacement from the horizontal axis and the displacement from the vertical axis. He viewed the perpendicular lines as horizontal and vertical axes. According to the story, Descartes was staring at a fly crawling on the ceiling when he realized that he could describe the fly’s location in relation to the perpendicular lines formed by the adjacent walls of his room. Plotting Ordered Pairs in the Cartesian Coordinate SystemĪn old story describes how seventeenth-century philosopher/mathematician René Descartes, while sick in bed, invented the system that has become the foundation of algebra.