The Lesson
A 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 Form
An 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. finding the slope from a linear equation
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The number on its own is the y-intercept.
y = 2x + 1The y-intercept is 1. finding the y-intercept from a linear equation
Other Forms of Linear Equations
There are other forms of linear equation.-
The general form of a linear equation is:
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. 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't
Now 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