Linear Equations (in Slope-Point 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:

y minus y 1 equals m (x minus x 1) On a graph, a linear equation looks like a line:

line on a graph
  • 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 Form

An example of a linear equation in slope-point form is given below:

y minus 2 equals 2 (x minus 1) If we compare this equation to y − y1 = m(x − x1), we can find the slope and a point on the line.

Other Forms of Linear Equations

There are other forms of 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 y-coordinate of a point.
  • the number that is subtracted from the x gives the x-coordinate of a point.
What if a number is added to the y or x?
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.
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See Also

What is a linear equation? What is the slope? What is the y-intercept? Finding the slope from a linear equation in slope-point form Finding the y-intercept from a linear equation in slope-point form