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Graphs of linear equations worksheet (with solutions)

Graphs of linear equations worksheet (with solutions)

Subject: Mathematics

Age range: 11-14

Resource type: Worksheet/Activity

Last updated

2 August 2026

pdf, 116.25 KB
pdf, 116.25 KB

A worksheet on matching graphs of linear functions to their equations. Answers are included.

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A bundle is a package of resources grouped together to teach a particular topic, or a series of lessons, in one place.

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Coordinate Geometry Bundle - Slope Gradient Midpoint Distance Line Worksheets

A bundle of 12 worksheets (with detailed solutions) on Coordinate topics appropriate for GCSE students. Each worksheet contains questions for students of various abilities. The topics covered by these worksheets include: * Midpoint of a line segment * The distance between two points on a line * Straight lines * Gradient and y-intercept of a straight line * Gradient of a straight line passing through two points * Equation of a line given its gradient and a point * Parallel and perpendicular lines * Equation of a line through a point and parallel to a given line * Equation of a line through a point and perpendicular to a given line * Graphs of linear equations * Special Cases of Linear Functions * Solving simultaneous equations graphically Master coordinate geometry with this comprehensive, no-prep straight lines worksheet pack! Perfect for KS3 and KS4 lessons, homework, and GCSE or IGCSE revision, this resource features targeted practice for finding the midpoint of a line segment, calculating the distance between two points, finding gradients, and writing linear equations for parallel and perpendicular lines. Includes full, step-by-step worked solutions! ________________________________________ Looking for a rigorous, completely no-prep math resource to help your students master straight lines and coordinate geometry? This comprehensive coordinate geometry resource pack is designed to fully align with UK GCSE and IGCSE math specifications. Whether you need structured cover lessons, targeted homework tasks, daily classroom practice, or an all-in-one exam revision booklet, this resource is ready to print and use immediately! Every single worksheet comes paired with a complete, fully worked step-by-step solution key. The answer keys explicitly demonstrate coordinate substitution, radical/surd length simplifications, gradient formula structures, and linear point substitutions—making marking an absolute breeze and enabling effective student self-assessment or peer-marking. ________________________________________ **What Skills & Topics Are Covered?** 1. **Midpoint of a Line Segment** • Calculating exact midpoints from pairs of positive and negative integer coordinates. • Scaffolded problem sets running from basic coordinates up to fractional and decimal midpoint values. 2. **Distance Between Two Points** • Applying the coordinate length formula to find the exact distance between points. • Working with algebraic variables (including a, b, and c coefficient lengths). • Calculating distance sets resulting in simplified surds and radicals. 3. **Geometric Applications of Distance** • Using coordinates to find the radius and coordinates of circles from standard endpoints or diameters. • Proving and classifying triangles (including isosceles and right-angled triangle verifications using the converse of Pythagoras' theorem). 4. **Gradient & Y-Intercepts** • Extracting the gradient and y-intercept directly from the standard equation of a straight line. • Rearranging multi-step linear functions into standard graphing form. • Calculating raw gradient strings passing directly through two given coordinate points. 5. **Writing Linear Equations** • Writing the full equation of a straight line given a specific gradient and passing point. • Generating full linear equations given only two starting coordinate points. 6. **Parallel and Perpendicular Lines** • Analyzing pairs of linear equations to determine if lines are parallel, perpendicular, or neither. • Evaluating identical gradient criteria and testing negative reciprocal properties. ________________________________________ **Why Teachers Choose This Resource Pack:** • Zero Prep Needed: Save hours of planning—just download, print, and you are ready to go! • Step-by-Step Solutions: Complete answer keys explicitly show the formulas and substitution paths, making it incredibly clear for visual learners. • Scaffolded Practice: Each topic seamlessly transitions from basic coordinate inputs up to advanced multi-step geometric proofs. • Clean, Accessible Layout: Minimalist design avoids visual clutter, keeping student focus entirely on the calculations and graphing structures. ________________________________________ **Curriculum Alignment & Target Groups:** • Key Stage 3 (KS3): Perfect foundational and extension blocks for Year 9. • Key Stage 4 (KS4): Ideal for Year 10 and Year 11 preparation across both Foundation and Higher GCSE/IGCSE tiers. • Exam Boards: Fully supports the curriculum objectives for AQA, Edexcel, OCR GCSE, and Cambridge CIE / Oxford AQA IGCSE exams.

£8.90
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Straight Line Graphs and Equations Worksheets Bundle with Answers

A collection of of seven on straight line graphs and equations of straight lines. Students will practice: * drawing graphs of linear equations * matching graphs of linear functions to their equations * identifying the gradient of a line passing from two given points * identifying the gradient and the y-intercept of a line given its equation * working out the equation of a line given two points on the line * working out the midpoint of line segments given their end points * finding the equation of a line that passes through a given point and has a given slope * finding the equation of a line that passes through a given point and is parallel to a given line * finding the equation of a line that passes through a given point and is perpendicular to a given line Detailed solutions to all worksheets are included. Master coordinate geometry with this comprehensive, no-prep **Straight Line Graphs and Equations Worksheets Bundle with Answers!** This pack provides a complete collection of straight line graphs worksheets and coordinate geometry exercises, helping secondary maths students build absolute confidence in linear relationships. Whether your classes are just learning how to calculate rise over run or revising for their final GCSE exams, this pack offers targeted practice across all visual and algebraic representations. Complete with a **fully worked step-by-step solutions guide**, it is perfect for classwork, homework, cover lessons, or independent revision. **What is Included?** * **Drawing Graphs of Linear Equations:** Step-by-step tasks where students complete tables of values and plot straight lines on coordinate grids. * **Matching Graphs with Equations:** Visual matching exercises that test student understanding of lines, fractional gradients, and vertical or horizontal lines. * **Finding Equations from Graphs:** Exercises requiring students to look at plotted straight lines and calculate their exact linear equations. * **Gradients from Two Points:** Practice worksheets focusing on applying the gradient formula to pairs of positive, negative, and zero coordinates. * **Stating Gradient and Intercept:** Tasks testing students on identifying gradients and y-intercepts from standard, fractional, or rearranged linear forms. * **Equations from Points or Gradients:** Guided practice for writing the full equation of a line when given structural boundaries like points or constant rates. * **Line Segment Midpoints:** Clear exercises to help students successfully compute the exact midpoints of directed line segments. * **Complete Solutions Guide:** A highly detailed answer key showing every calculation step, making student self-marking easier than ever. **Key Concepts Covered** * Completing algebraic input-output tables to plot linear graphs on axes * Applying the gradient formula to positive and negative integer coordinate points * Isolating variables to transform linear equations into standard gradient-intercept form (y = mx + c) * Finding visual and mathematical rise over run directly from coordinate grids * Working out the exact midpoints of coordinates across all four quadrants **Curriculum Alignment** This resource directly supports algebraic reasoning and linear functions across secondary stages, aligning closely with: * **UK National Curriculum:** Key Stage 3 and Key Stage 4 Mathematics (Graphs of linear functions, finding gradients, midpoints, and formulating equations). * **GCSE Maths:** Essential Foundation and Higher tier preparation for linear graphs and coordinate geometry (AQA, Edexcel, and OCR). **Why Teachers Love This Resource** * **Zero Prep Required:** Just download, print the sheets, and hand them out to your classes immediately. * **Differentiated Scope:** Moves fluidly from basic coordinate grid plotting to multi-step algebraic manipulation. * **Perfect for Cover Lessons:** The highly detailed solutions guide lets cover teachers, parents, or students quickly trace exactly where a maths error occurred.

£6.50
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Equations and graphs of straight lines Bundle

A collection of three worksheets. One worksheet on determining whether a point is on a line with a given equation by substituting the coordinates of the point on the equation. One worksheet on determining the gradient and the y-intercept of a straight line from its equation. And one worksheet on matching graphs of linear functions to their equations. Answers are included.

£2.90
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Graphs of Linear Equations-Graphical Solution of Simultaneous Equations Bundle

A collection of three worksheets. One worksheet on matching graphs of linear functions to their equations and two worksheets on solving simultaneous equations using their graphs. Detailed solutions are included.

£2.90
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Linear Equations: Slope-Intercept Form and Graphs Worksheets (with solutions)

A collection of three worksheets on the following: * writing linear equations in slope-intercept form by rearranging them * matching graphs of linear functions to their equations * drawing graphs of linear equations. Solutions are included.

£2.65

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