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What Is a Linear Equation (in Slope-Point Form)? (Mathematics Lesson)

What Is a Linear Equation (in Slope-Point Form)?

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.

Interactive Test
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Here's a second test on linear equations in slope-point form.
Here's a third test on linear equations in slope-point form.

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.