Graphing linear Equation
A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. If you are given a simple equation and have been asked to visualize it, you will very likely able to do it mentally.
Now, if the equation gets more complex, you will soon find it difficult to visualize it mentally. This is where the coordinate plane is here to help.
With several simple steps, you will be able to draw out any equation. As a start, we will use the equation for straight lines.
Note that, straight line equation is also known as linear equation. You need to draw a x-y table to help you to record the coordinates of your points in orderly manner. Take note on how the coordinates of each point are calculated. In this lesson, only few points are used to plot the equation. For more complicated equations, you may need to get more points to have a complete picture of the equation. The position of a point in a plane is fixed by selecting two axes of reference which are formed by combining two number lines at right angles so that their zeros coincide.
The horizontal number line is called x-axis and the vertical number line is called y-axis. ax + b = 0 is a linear equation in one variable.
The graph of x = a is a line parallel to y-axis at x=a. The graph of y=b is a line parallel to x-axis at y = b.
In order to graph using point plotting, you will need to create a table. You will need to choose at least 3 numbers for x and plug them into the equation to find corresponding y values . To graph using intercepts, you will need to find both the X and the y intercept To find the x-intercept , substitute 0 for y and solve for x To find the y - intercept , substitute 0 for x and solve for y. To graph a linear equation, you will need to find the slope and the y-intercept for the equation. Remember: y = m x + b slope Y-intercept (the point where the graph crosses the y-axis)
When the slope, m, is positive, the line slants upward to the right. The more positive m is, the steeper the line will slant upward to the right.
When the slope is negative, the line slants downward to the right, and, as the slope becomes more and more negative, the line will slant downward steeper and steeper to the right.
Also, notice that when the y-intercept, b, is positive, the line crosses the y-axes above y = 0. When b is negative, the line crosses the y-axis somewhere below y = 0. In fact, b is the value on the y-axis where the line passes through this axis. The line intercepts, or crosses, the y-axis here, and, therefore, b is called the y-intercept.
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