Mathematics-Monster.com
(#mm)

menu

Finding the Slope from a Linear Equation in Slope-Point Form
(KS3, Year 9)

homelinear equationsfinding the slope from a linear equation in slope-point form
The slope of a line is its steepness. It is how far up a line goes compared to how far across it goes. The line below has a slope of 2 because it goes up 2 units for every 1 unit it goes across. The slope of the line is 2 because it goes up 2 units for every 1 it goes across A line can be represented by a linear equation. We can find the slope from a linear equation.

Real Examples of Finding the Slope from a Linear Equation in Slope-Point Form

Finding the slope of a line from a linear equation in slope-point form is easy. Here are some linear equations, which represent lines. We show how to find the slope from the linear equation.
  • The slope of y − 4 = 2(x − 1) is 2. slope of y minus 4 equals 2 (x minus 1) is 2 Look at the number in front of the brackets with the x in it. This is the slope. A slope of 2 means that the line will go up by 2 when it goes across by 1.
  • slope of y − 1 = −3(x − 3) is −3. slope of y minus 1 equals minus 3 (x minus 3) is minus 3 The number in front of the brackets is negative. This means the line slopes downwards. A slope of −3 means that the line will go down by 3 when it goes across by 1.

Lesson Slides

A linear equation (in slope-point form) is given in the form below: y − y1 = m(x − x1) The m gives the slope of the line. The slider below explains why the m in a linear equation gives the slope:

Beware

Be Careful

In this lesson, we have said that the slope is given by the number in front of the brackets with the x in it. This is true as long as the x in the brackets is positive and doesn't have another number in front of it. For example, consider the linear equations shown below:
  • The x has a − sign in front of it:
    y − 1 = 2(−x − 1)
    The slope would be −2.
  • The x has a number front of it:
    y − 1 = 2(3x − 1)
    The slope would be 6 (2 × 3).

Note

Postive And Negative Slopes

A positive slope means the line slopes up and to the right: positive slope A negative slope means the line slopes down and to the right: negative slope

Zero Slope And Undefined Slope

A line that goes straight across has zero slope: Flat lines have zero slope A line that goes straight across has an undefined slope: Lines that go straight up have an undefined slope
author logo

This page was written by Stephen Clarke.

You might also like...

Help Us Improve Mathematics Monster

  • Do you disagree with something on this page?
  • Did you spot a typo?
Please tell us using this form.

Find Us Quicker!

  • When using a search engine (e.g., Google, Bing), you will find Mathematics Monster quicker if you add #mm to your search term.

Share This Page

share icon

If you like Grammar Monster (or this page in particular), please link to it or share it with others.

If you do, please tell us. It helps us a lot!

Create a QR Code

create QR code

Use our handy widget to create a QR code for this page...or any page.