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Linear Equations (in SlopePoint Form)
(KS3, Year 9)
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.
 (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:
Read more about the general form of a linear equation 
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
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.
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 ycoordinate is −1.
When a number is added to y or x, the coordinate is negative.
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