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

Slope of a Line

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.

Positive Acute Angle

If m < 0, the function is decreasing and the angle between the line with the positive x-axis is obtuse.

Negative Obtuse Angle

Two parallel lines have the same slope.

Parallel Lines

n is the y-intercept and indicates the intersecting point of the line with the vertical axis.

Y-intercept


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

Linear Function


Identity Function

y = x

Its graph is the bisector of the first and third quadrant.

Identity Function


Examples

1 y = 2x - 1

x y = 2x-1
0 -1
1 1

Linear Function

2y = -¾x - 1

x y = -¾x-1
0 -1
4 -4

Linear Function