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.
- (x1, y1) is a point on the line.
A Real Example of a Linear Equation in Slope-Point FormAn example of a linear equation in slope-point form is given below:
If we compare this equation to y − y1 = m(x − x1), we can find the slope and a point on the line.
The number in front of the brackets is the slope.
y − 2 = 2(x − 1)The slope is 2. Read more about finding the slope from a linear equation in slope-point form
A point on the line can be found from the numbers being subtracted from y and x.
y − 2 = 2(x − 1)1 is being subtracted from x. 1 is the x-coordinate of the point. 2 is being subtracted from y. 2 is the y-coordinate of the point. The point on the line is (1, 2). Read more about finding the y-intercept from a linear equation in slope-point form
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-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
When Points Have Negative CoordinatesIn this lesson, we have said that:
- the number that is subtracted from the y gives the y-coordinate of a point.
- the number that is subtracted from the x gives the x-coordinate of a point.
y + 1 = ...Remember, that subtracting a negative number is the same as adding the positive number:
y + 1 = y − −1...−1 is being subtracted from y, so the y-coordinate is −1. When a number is added to y or x, the coordinate is negative.