The LessonA linear equation is an equation that represents a line. A linear equation can be written in the form:
On a graph, a linear equation looks like a line:
- y and x are the Cartesian coordinates of points on the line.
- m is the slope of the line. It tells you the steepness of the line.
- c is the y-intercept of the line. It tells you the y-coordinate of where the line crosses the y-axis.
A Real Example of a Linear Equation in Slope-Intercept FormAn example of a linear equation in slope-intercept form is given below:
If we compare this equation to y = mx + c, we can find the slope and y-intercept.
The number in front of the x is the slope.
y = 2x + 1The slope is 2. Read more about finding the slope from a linear equation
The number on its own is the y-intercept.
y = 2x + 1The y-intercept is 1. Read more about finding the y-intercept from a linear equation
Other Forms of Linear EquationsThere are other forms of linear equation.
The general form of a linear equation is:
Read more about the general form of a linear equation
The slope-point form of a linear equation is:
m is the slope of the line, and the point (x1, y1) is a point (in Cartesian coordinates) on the line. Read more about the slope-point form of a linear equation
Understanding What a Linear Equation Is...Let's see what parts a linear equation can have:
A linear equation can contain:
- Variables (such as y and x above)
- Constants (such as 1 above)
- Coefficients - a constant in front of a variable (such as 2 above)
...And What It Isn'tNow let's see what a linear equation cannot have. If you see any of these, it isn't a linear equation.
The variables in the linear equation (the y and x) cannot contain:
- Exponents - variables can only appear as x and y, not as x2 or y3
- Roots - variables cannot appear as √x or ∛y