Standard form of a linear function

The standard form of a lineal funtion is the equation of the line:

y = mx + b

Where, m is the slope of the line and b is the point where the line intersects the y-axis.

Therefore, a linear equation could easily be represented in the standard form of a linear function.

Example 1: Bring the following equation to the standard form of a linear function: y = 2x - 1

This equation is already in the standard form, therefore, its slope is m = 2 and its cut-off point with the y-axis is b = - 1.

Lineal function example 1

Example 2: Bring the following equation to the standard form of a linear function: 5y + 10x = 15

This equation is not in the standard form, we must clear and to obtain the standard form:

5 (y + 2x) = 15

y + 2x = 15/5

y = - 2x + 3

Lineal function example 2

This function or line has slope m = -2 and cuts the y-axis at b = 3.

Example 3: Bring the following equation to the standard form of a linear function: y / 4 - x / 16 = - 2

We must clear and so that it has the standard form:

1/4 (y - x / 4) = - 2

y - x / 4 = -2 · 4

y = x / 4 - 8

Lineal function example 3

This equation is in the standard form of a linear function, its slope is m = ¼ and it cuts with the y axis at b = -8.