Linear Equations (in General Form)
(KS3, Year 9)
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.
- a, b and c are constants. They have no meaning.
A Real Example of a Linear Equation in General FormAn example of a linear equation in general form is given below:
In this example, a = 4, b = 2 and c = 8. We can not directly tell anything about this line from this equation. We can use algebra to convert this equation from general form to slope-intercept form, and then find the slope and y-intercept:
4x + 2y + 8 = 0
2y = −4x − 8
y = −2x − 4
Read more about converting a linear equation in general form to slope-intercept form
Read more about finding the slope from a linear equation in general form
Read more about finding the y-intercept from a linear equation in general form
Other Forms of Linear EquationsThere are other forms of linear equation.
The slope-intercept form of a linear equation is:
m is the slope and c is the y-intercept.
Read more about the slope-intercept 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
Interactive WidgetYou can use this interactive widget to create a graph of a linear equation in the slope-intercept form. Use the buttons to change the values of the linear equation.
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