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Gradient Of A Line Worksheet

Gradient Of A Line Worksheet

Help your students prepare for their Maths GCSE with this free gradient of a line worksheet of 30+ questions and answers

  • Section 1 of the gradient of a line worksheet contains 20+ skills-based gradient of a line questions, in 3 groups to support differentiation
  • Section 2 contains 3 applied gradient of a line questions with a mix of worded problems and deeper problem solving questions
  • Section 3 contains 3 foundation and higher level GCSE gradient of a line exam questions 
  • Answers and a mark scheme for all gradient of a line questions are provided
  • Questions follow variation theory with plenty of opportunities for students to work independently at their own level
  • All questions created by fully qualified expert secondary maths teachers
  • Suitable for GCSE maths revision for AQA, OCR and Edexcel exam boards

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Gradient of a line at a glance

 

The gradient of a line tells us how steep that line is, the bigger the gradient, the steeper the line. A line with a positive gradient slopes upwards from left to right and a line with a negative gradient slopes downwards. When the equation of a straight line is written in the form y=mx+c, the value m is the gradient of the line. Straight line graphs are also known as linear graphs as their equations contain terms in x,y and constants only, with no higher powers of x or y. 

 

The gradient of a straight line can be calculated by taking any two points on the line, subtracting the y values, subtracting the x values and then dividing them. 

 

Since the gradient of a line tells us how steep the line is, parallel lines have equal gradients. The gradients of perpendicular lines – lines which meet at right angles – are negative reciprocals of each other. 

 

Horizontal and vertical lines have slightly adapted equations. Lines of the form y=a (where a is a constant) are straight horizontal lines with a gradient of 0. Lines of the form x=a (where a is a constant) are straight vertical lines and have a gradient of ∞.

 

When drawing straight line graphs, we can either use a table of values calculated using the equation of the line, or we can use information about the y intercept and the gradient of the line. The y intercept tells us the y coordinate of the point where the line crosses the y axis and the gradient tells us how many steps to go up for every one we go across. We can start drawing our line from the given point on the y axis and move across and up/down by the appropriate amount between each point on the line.

 

Looking forward, students can then progress to additional algebra worksheets, for example a simplifying expressions worksheet or simultaneous equations worksheet.

 

 

For more teaching and learning support on Algebra our GCSE maths lessons provide step by step support for all GCSE maths concepts.

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Lessons are selected to provide support where each student needs it most, and specially-trained GCSE maths tutors adapt the pitch and pace of each lesson. This ensures a personalised revision programme that raises grades and boosts confidence.


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