Linear Function
The equation of a linear function is:
y = mx + b
Its graph is an oblique straight line, which is defined by two points of the function.
y = x + 4
| x | 0 | -4 |
|---|---|---|
| y = x + 4 | 4 | 0 |
m is the slope of the straight line.
The slope is the inclination of the line with respect to the x-axis.
If m > 0, the function is increasing and the angle of the line with the positive x-axis is acute.
If m < 0, the function is decreasing and the angle between the line with the positive x-axis is obtuse.
Two parallel lines have the same slope.
n is the y-intercept and indicates the intersecting point of the line with the vertical axis.
If b = 0, the equation of a linear function is:
y = mx
Its graph is a straight line passing through the origin.
y = 2x
| x | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| y = 2x | 0 | 2 | 4 | 6 | 8 |
Identity Function
y = x
Its graph is the bisector of the first and third quadrant.
Examples
1 y = 2x - 1
| x | y = 2x-1 |
|---|---|
| 0 | -1 |
| 1 | 1 |
2y = -¾x - 1
| x | y = -¾x-1 |
|---|---|
| 0 | -1 |
| 4 | -4 |
