A linear equation expresses an equality between two expressions, one or both of which has a variable raised to the first power. In a linear equation, the expressions must have no more than two variables; the variables cannot be multiplied or divided by one another; and they cannot be found underneath a root or radical sign. You must be able to rearrange the equation into the form ax + by = c, where a, b and c are constants, and x and y are variables.
A linear equation in standard form can be written as ax + by = c. Although there must be two variables, y can equal zero, meaning you can rewrite the equation as ax + b = c. A is always positive and must be written as an integer. If a is negative, multiply every term by -1. If it is fractional, multiply each term by the inverse fraction to convert the number to 1.
To graph linear equations on the Cartesian plane, you must know the slope and y-intercept of the line. The slope-intercept form of the linear equation, y = mx + b, gives you this information. M equals the slope of the line, or the change in y value divided by the change in x value. B is where the line crosses the y-intercept. When a linear equation is in this form, you can predict many of the line's properties. For example, if m is large, the line will rise steeply. If m is positive, it will rise from left to right. If b is positive, the line will cross the y-axis above the x-axis. If it is negative, it will cross below the x-axis.
The point-slope form of linear equations includes the value of the slope and the coordinates of a point on the line. It appears in the form y - y1 = m(x - x1), where (x1, y1) are the coordinates of a point on the line and m equals the slope. While you cannot graph a linear equation using this line, you can convert it into slope-intercept form by substituting the values of m, x1 and y1 into the slope-inercept equation and solving for b.