![[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],line is called the y-axis. Arrowheads At each end of both axes indicate the infinity of the set of real numbers. Notice that the axes divide the plane into four regions or quadrants labeled with Roman numerals. I through IV in counterclockwise direction. The first number x is called x coordinate or abscissa and the second number y is called the y Coordinate or ordinate . ,[object Object],the 17 th -century French philosopher and mathematician who first devised the coordinate system . 4 3 2 1 -1 -2 -3 -4 -1 -2 -3 -4 1 2 3 4 y x I 11 111 1V](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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- 3. 5.2 “ Points in the Cartesian Coordinate Plane” There exist a one-to-one correspondence between points in the plane and the ordered pairs of real numbers. 5.2.1 “The coordinates of a point” The distance of a point from the x- and y-axes is measured in units from the point along the line perpendicular to the respective axis. 5.2.2 “Plotting of Points” If points in a coordinate plane can be named. Points can also be plotted in the plane given their coordinates. To locate the P represented by the ordered pair (3,4). Point the tip of your pencil at the origin (0,0) move it 3 units to the right, then 4 units upward your point is at P is 3 and the y-coordinate x-coordinate is 4. The process of locating a point in the coordinate plane is called plotting the point. 5.2.3 “ Points in a Quadrants” Given coordinates of a point, the quadrant where it is located can be determined. In a quadrant I, both abscissa and ordinate are positive (x, y). In quadrant II, the abscissa is negative while the ordinate is positive, (x, y). In quadrant III, both abscissa and ordinate are negative, (x, y). Points found on any of the axes are not considered to be in any quadrants.
- 5. 5.3.3 “ Properties of the Graph of a Linear Equation Ax + By = C” The graph of every equation of the form Ax + By = C, where a and b are not both zero, is a line. In studying of this equation, there are properties of the graph that have to be considered. 5.3.3a “ The Intercepts” The set of ordered pairs which satisfies the equation are (-3, 4), (3, 0), (6, -2).The point whose coordinates consist the number pair (0, 2) intersects the y-axis, thus the ordinate 2 point whose coordinates consist of the number pair (3, 0) intersects the x-axis, thus the abscissa 3 of this point is called the x-intercepts. Remember: The x- intercept is the abscissa of the point (a, 0) Where a graph intersects the axis. The y-intercept is the ordinate of the point (0, b) Where a graph intersects the y-axis. 5.3.3b “ The Slope of a Line” The graphs of the equations y = 3x + 1 and y = x + 1 are drawn. Using the marked points on the graph, the ratio of the vertical distance to the horizontal distance between two points can be found. y x y = x + 1 y = 3x + 1 2 (rise) 2 (run) If you take the points (0, 1) and (-1, -2) on the line y = 3x + 1, the vertical distance is 3 units and the horizontal distance is 1 Unit or vertical distance (rise ) = 3 or 3 horizontal distance (run) 1 The equation y = 3x + 1 where 3/1 stands for the slope.