In this publication, we will consider what a linear function is, and also give its formula and graph. The information presented is accompanied by practical examples for better understanding.
Linear function definition
Linear function is a function that looks like
- x – independent variable (argument);
- a и b are arbitrary numbers.
Substituting specific values into this formula x, we can calculate their corresponding values y.
Example: wise function y = 2x – 3. Let’s create a lookup table for it. x и y.
| 0 | -3 | 2 0 — 3 = -3 |
| 1 | -1 | 2 1 — 3 = -1 |
| 2 | 1 | 2 2 — 3 = 1 |
| 3 | 3 | 2 3 — 3 = 3 |
Linear function graph
Linear function graph y = ax + b is a continuous straight line. However, it can be:
- increasing at a > 0 (meaning y increases monotonically).
- decreasing at a <0 (y decreases monotonically).
Note:
- with a = 0 straight line parallel to the x-axis (Ox);
- with b = 0 the function line passes through the origin.
In order to plot a function graph, it is enough to calculate the coordinates of two points using its formula. For the above example
Now let’s plot a function with a negative value aFor example,
- x = 0, y = -3 ⋅ 0 + 5 = 5
- x = 2, y = -3 ⋅ 2 + 5 = -1
Now let’s draw a straight line through the obtained points: (0, 5) and (2, -1).
