The point at which the x and y-axis intersect is known as the origin. $$2y-4x\, $$įrom here you can graph the equation as we did in the example above. A coordinate plane is a two-dimensional plane formed by the intersection of the x-axis and the y-axis. The standard form of a linear equation isīefore you can graph a linear equation in its standard form you first have to solve the equation for y. The x-intercept is found by finding the value of x when y = 0, (x, 0), and the y-intercept is found by finding the value of y when x = 0, (0, y). This linked algebra and geometry through the use of graphs. For example, a linear equation like y 2x + 1 could be plotted as a line on the coordinate plane, while a quadratic equation like y x2 could be plotted as a parabola. The point in which the graph crosses the x-axis is called the x-intercept and the point in which the graph crosses the y-axis is called the y-intercept. This enabled the visualization of algebraic equations in geometric form. If you only want to use two points to determine your line you can use the two points where the graph crosses the axes. A discrete function consists of isolated points.īy drawing a line through all points and while extending the line in both directions we get the opposite of a discrete function, a continuous function, which has an unbroken graph. Now you can just plot the five ordered pairs in the coordinate planeĪt the moment this is an example of a discrete function. 2, -1, 0, 1 and 2 and calculate the corresponding y values. When choosing your points try to include both positive and negative values as well as zero.īegin by choosing a couple of values for x e.g. If you want to graph a linear equation you have to have at least two points, but it's usually a good idea to use more than two points.
If all variables represent real numbers one can graph the equation by plotting enough points to recognize a pattern and then connect the points to include all points. The graph of the linear equation is a set of points in the coordinate plane that all are solutions to the equation.
A linear equation is an equation with two variables whose graph is a line. This page titled 5.19: Quadrilateral Classification in the Coordinate Plane is shared under a CK-12 license and was authored, remixed, and/or curated by CK-12 Foundation via source content that was edited to the style and standards of the LibreTexts platform a detailed edit history is available upon request.