Linear function is called function of a type of y = k * x + b. Graphically it is represented by a straight line. Functions of such look are widely applied in physics and the equipment for representation of dependences between various sizes.

## Instruction

1. Let function of a general view of y = be given to k * x + by b where k ≠ 0, b ≠ 0. For creation of the schedule linearof functions there are enough two points. For descriptive reasons and the accuracy of construction find five points of the set function: x =-1; 0; 1; 3; 5. Substitute these values in the set expression for function and calculate values y: y = - k + b; b; k + b; 3 * k + b; 5 * k + b. Further draw horizontal abscissa axis (axis x) and vertical ordinate axis (axis y). Note on the turned-out coordinate plane the found couples of points (-1, - k + b), (0, b), (1, k + b), (3, 3 * k + b), (5, 5 * k + b). For this purpose at first find the required value on axis x, and then postpone the corresponding value for axes y. Then draw the straight line connecting all designated points.

2. Construct the schedule of the following function: y = 3 * x + 1. Calculate values of coordinates of y for the following points x =-1, 0, 1, 3, 5. For example, for a point with coordinate x =-1: y = 3 * (-1) + 1 =-3 + 1 =-2. The point turns out (-1,-2). Similarly for other points: (0, 1), (1, 4), (3, 10), (5, 16). Now note these points on the coordinate plane. Through the turned-out points draw a straight line.

3. For linear functions special cases are possible. Pay attention to the most widespread. First, y = const. In this example the value of coordinate of y is constant for any value of coordinate x. In the traditional system of coordinates (axis x – horizontal, axis y – vertical) the schedule of similar function looks as a horizontal straight line.

4. Secondly, x = const. Here for any value of coordinate of y value x always constant. I.e. the schedule looks as a vertical straight line.