A linear equation is an equation that makes a line when graphed. A linear equation can be represented by an equation in the form ax + by = c.
Figure 1 is an example of a linear equation and its graph.
Figure 1: The linear equation y = 2x - 3 and its graph. |
Name | Equation | Parameters | Notes |
---|---|---|---|
Standard form | ax + by = c | a, b and c | All lines can be expressed in this form. This form is used in linear systems to make it easier to use matrices. |
Slope-intercept form | y = mx + b | m is the slope, b is the y-intercept. | Vertical lines can not be expressed in this form, as their slope is undefined. |
Point-slope form | y = m(x - x_{0}) + y_{0} | m is the slope of the line, (x_{0}, y_{0}) is the coordinate of any point on the line. | This form is useful when the coordinate of a single point on the line is known along with the slope. Vertical lines can not be expressed in this form as their slope is undefined. |
Two point form | (x_{1}, y_{1}) and (x_{2}, y_{2}) are the coordinates of two distinct points on the line. | This form is useful when the coordinates of any two distinct points of a line are known. Vertical lines can not be expressed in this form as (x_{2} - x_{1}) is 0, and division by zero makes the equation undefined. | |
Vertical line | x = x_{0} | x_{0} is the x-intercept. | Only vertical lines can be expressed in this form. |
Horizontal line | y = y_{0} | y_{o} is the y-intercept. | Only horizontal lines can be expressed in this form. |
Table 1: Forms of linear equations. |
# | A | B | C | D |
E | F | G | H | I |
J | K | L | M | N |
O | P | Q | R | S |
T | U | V | W | X |
Y | Z |
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