![]() Consequently, the line being graphed must cross the vertical axis 3 units above the horizontal axis and it must rise vertically 2 units for every 1 unit it runs horizontally. According to the y = mx + b formation of a line, m = 2 and b = 3. For example, if x = 0, y must equal 3 if x = 1, y must equal 5 etc. One means to do this would be to manually generate a list of points that satisfy this equation. Graph the series of points satisfying the equation y = 2x + 3 The standard form in which linear equations which are graphed appear on a coordinate plane is: Since this is important, it bears repeating: a line on a coordinate plane is a graphical representation of a series of points that fulfill a mathematical equation. It is the line that graphs out all the points that satisfy this equation. The location and slant of a line is determined by an equation. In the above coordinate planes, the lines appeared without any explanation as to why the line pointed in a certain direction at a certain steepness. There are four types of slope: positive, negative, zero, and undefined. In the above graph, point A is at (-8, 4) and point B is at (8, -4). Rise over run refers the change of the rise (y values) of any two points on the line over the change in the run (x values) of the same two points on the line. Every line has a slope defined by rise over run (i.e., the amount the line rises vertically over the amount the line runs horizontally). One property of a line is its slope, which is a measure of the steepness of the line. The chart below depicts the sign of x and y. In the first quadrant, both x and y are positive while in the second quadrant x is negative and y is positive. In this case, the other quadrants still exist, but they are merely not shown). ![]() (Note: Some graphs only show one quadrant. The origin is point E in this graph.Įach coordinate plane is divided up into four quadrants, labeled below. Origin - The point in the center of the coordinate plane where the x and y axis intersect (0, 0). ![]() Similarly, point C is at (-6, -2) since it is horizontally 6 units to the left of the center and it is vertically 2 units below the center. The proper notation is: (X, Y) where (0, 0) is the intersection of the x and y-axis.įor example, point A is at (2, 4) since it is horizontally 2 units to the right of the center and it is vertically 4 units above the center.
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