Equation of Straight Line Graphs

To find the equation of straight line graphs students need to calculate the gradient using two pairs of coordinates and the intercept which is the y value of where it crosses the vertical axis.  Examiner’s reports of past exam questions show students are more able to find the intercept of a straight line than they are at calculating the gradient.  This lesson on interpreting straight line graphs is available here.

Equation of a line using coordinate pairs

Equation of Straight Line Graphs

The starter recaps the learning in the previous lesson on using graphs to solve equations by interpreting the x and y values of a line. By adding the x and y values together students can see the equation of the line is x + y = 5.

As an extension I ask the class to imagine the line extended beyond the grid and to show me other coordinate pairs the line would pass through.  We have a short discussion about coordinate pairs with decimal numbers and move on to the main teaching part.

Finding the equation of straight line graphsEquation of Straight Line Graphs

To introduce the main part of the lesson we discuss how the steepness (gradient, M) and position (intercept, C) of where the line crosses the y axis define how the graph looks on a grid.   Equations of linear graphs can be written in the form y = mx + c.

The gradient (M) can be calculated using two coordinates that lie along a line.  The gradient is the change in vertical distance divided by the change in horizontal distance.  This gives a measure of the steepness of the line.

The intercept (C) is the point where the line crosses the y axis.  The intercept can also be defined algebraically as the value of y when x = 0.

Explaining how to find the equation of straight line graphs

I work through the first two examples on the second slide with the class and encourage the students to attempt the third question on their mini-whiteboards.  If more practice is needed I use the Interactive Excel File to generate further questions.  When they are ready students work through the questions on the third slide independently.  All the answers are provided in the lesson plan.

Extending the learning in the plenary

Equation of Straight Line Graphs

The plenary extends the learning because the line now has a fractional gradient, negative intercept and students need to choose their own coordinates to use.

Rather than calculating the gradient they are asked to explain why it is 2/3.  To do this they simply use the method as before leaving the answer as a fraction.  I encourage students to use two sets of coordinates, so they can check their working.  This also consolidates their method.  The equation of the straight line is y = (2/3)x – 1.

The next lesson in the Functions, Graphs and Equations unit goes onto plotting quadratic graphs from a table of results where students explore the properties of parabolas.

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes:

<a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Mr Mathematics Blog

Angles in Polygons

There are two key learning points when solving problems with angles in polygons.  The first is to understand why all the exterior angles of a polygon have a sum of 360°.  The second is to understand the interior and exterior angles appear on the same straight line. Students can be told these two facts and […]

Getting Ready for a New School Year

When getting ready for a new school year I have a list of priorities to work through. Knowing my team have all the information and resources they need to teach their students gives me confidence we will start the term in the best possible way.  Mathematics Teaching and Learning Folder All teachers receive a folder […]

Mathematics OFSTED Inspection – The Deep Dive

Earlier this week, my school took part in a trial OFSTED inspection as part of getting ready for the new inspection framework in September 2019. This involved three Lead Inspectors visiting our school over the course of two days. The first day involved a ‘deep dive’ by each of the Lead Inspectors into Mathematics, English […]