Linear equation with two variables

A linear equation with two variables can be written in the following way:

ax + by = c

Where, x and y are two variables to the first power. The constants a, b, c are real numbers, with a ≠ 0 and b ≠ 0.

Graphically, these type equations are straight lines.

Graphs of linear equations of two variables

To obtain the graph of this type of equations we will rely on the canonical equation of a line, which has the following form:

x / a - y / b = 1

Where, a and b are the cut points with x axis and y axis respectively.

Linear equations example

Example 1: Graph the following linear equation: 4x - 8y = 2.

First, we must bring this equation to the canonical expression of the line. Therefore, to obtain the number 1 of said expression (which appears after equality) we divide by 2 both sides of equality:

4x / 2 - 8y / 2 = 2/2

2x - 4y = 1

From here we see that:

2x / 1 - 4y / 1 = 1

If we invert the quotients of the equation, we can find the cut points with the axes:

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

This would be the canonical expression. The graph of the linear equation will be:

Linear equations example 2

Example 2: Graph the following linear equation: 5x - 9y = 3.

First, we must bring this equation to the canonical expression of the line. We divide 3 sides of equality by 3:

5x / 3 - 9y / 3 = 3/3

5x / 3 - 3y = 1

From here we see that:

5x / 3 - 3y / 1 = 1

If we invert the quotients of the equation, we can find the cut points with the axes:

x / (3/5) - y / (1/3) = 1

The graph of our equation will be:

Linear equations example - 3