What Is a Linear Equation (in SlopePoint Form)? (Mathematics Lesson)
What Is a Linear Equation (in SlopePoint Form)?
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.

(x_{1}, y_{1}) is a point on the line.
A Real Example of a Linear Equation in SlopePoint Form
An example of a linear equation in slopepoint form is given below:
If we compare this equation to y − y_{1} = m(x − x_{1}), 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 slopepoint 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 xcoordinate of the point.
2 is being subtracted from y. 2 is the ycoordinate of the point.
The point on the line is (1, 2).
Read more about finding the yintercept from a linear equation in slopepoint form
Other Forms of Linear Equations
There are other forms of linear equation.

The general form of a linear equation is:

The slopeintercept form of a linear equation is:
m is the slope and c is the yintercept.
Read more about the slopeintercept form of a linear equation
Interactive Test
showHere's a second test on linear equations in slopepoint form.
Here's a third test on linear equations in slopepoint form.
Beware
When Points Have Negative Coordinates
In this lesson, we have said that:

the number that is subtracted from the y gives the ycoordinate of a point.

the number that is subtracted from the x gives the xcoordinate of a point.
What if a number is added to the y or x?
Remember, that subtracting a negative number is the same as adding the positive number:
−1 is being subtracted from y, so the ycoordinate is −1.
When a number is added to y or x, the coordinate is negative.