Build a graph straight?
Mathematics is not an easy science, and not everyone is given the first time. Sometimes students sit behind notes for several hours, only to finally understand how to build a straight line graph, although in reality there is nothing difficult here: you just need to carefully deal with all the elements of the equation and understand the technology of solving an equation that can be plotted on a graph in the form of a straight line.
Simple Equation Chart
The simplest equation on which it is desirable to learn to build lines on a graph is y = kx + b. In this case, it is clear that y depends linearly on x, and the solution of the equation can be known graphically. To do this, first choose two points on the line and call them A and B. In order not to suffer for a long time with the construction, it is best to place these points at the intersections with the axes.
Determination of coordinates
Now it is necessary to determine on which coordinates these points are located. To do this, we lower the perpendicular lines from the points to the coordinate axis. The numbers on the scale are the coordinates of points A and B. For example, the coordinates of point A are (2; 3), and the points B are (-2; 0).After that, we substitute the obtained data into the general equation. Then for A we get 3 = 2k + b, and for point B - 0 = -2k + b. Accordingly, we have a system of two equations, where the unknowns are k and b.
Solving a system of equations
- Such a system can be solved in any way convenient for you. In the case of the example, two equations can be added, since in both parts of the system the coefficient k is unknown, and the remaining coefficients are equal in magnitude, although they are opposite in sign. Then we get that 3 + 0 = 2k - 2k + b + b. Simplify the equation and get 2b = 3. From here we get that b = 3/2. Then we substitute this value of the element b into any equation and find k. We get: 0 = -2k + 3/2, from which we deduce that k = 3/4.
- Now we can substitute the value of the coefficients k and b into the original equation, and we obtain the equation of a straight line, which we should have found. So, it looks like y = 3x / 4 + 3/2.
By this principle, almost any linear equation can be solved. The algorithm remains the same - only the variables change. The main thing in this form of linear equations is to make a graph correctly and indicate points. After that, it remains only to determine the coordinates and substitute the data into the equation, making up the system. The coefficient k is the slope of the line.Trigonometrically, this coefficient can be defined as the tangent of the angle between the x axis and the straight line. The unknown y in such an equation is a variable, just like x.
If even with the help of the above instructions, it is impossible to determine the equation of a straight line, then you can use the function to build an online straight line graph. On the Internet, you can find many sites on which it is enough to enter the equation given to you, and in a few moments you will receive a complete solution, a ready-made graph and a final equation.
You will only need to rewrite this automatic solution in a notebook, but it is better, of course, to deal with solving such equations on your own, since mathematics is a very important science, without which no calculations can exist.
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