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Equation of a line given its gradient and a point worksheet (with solutions)

Equation of a line given its gradient and a point worksheet (with solutions)

Subject: Mathematics

Age range: 11-14

Resource type: Worksheet/Activity

Last updated

2 August 2026

pdf, 88.81 KB
pdf, 88.81 KB

A worksheet on determining the equation of a straight line given its gradient and a point on it. Solutions are provided.

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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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Linear Equations Bundle: Slope, Writing Equations, Parallel & Perpendicular

Three worksheets on the following: * finding the gradient of a line given the coordinates of two points * determining the equation of a straight line given its gradient and a point on it * determining whether two lines are parallel, intersecting or coinciding and examining if they are perpendicular The exercises require to find the gradient of a line given the coordinates of two points on it using the relevant formula, determine the equation of a line given its gradient and a point on it, find the relative position of two lines given their equations (by considering their gradients), examine whether two lines are perpendicular given their equations (by considering their gradients), find the equation of a line parallel or perpendicular to another line, find a missing parameter in an equation of a line given that it is parallel or perpendicular to a given line and passing through a given point and find the relative positions or equation of three lines given their graph. Very detailed solutions included. Master linear graphs with this comprehensive worksheet bundle. Ideal for Key Stage 3, Key Stage 4, and GCSE Maths. Includes targeted practice pages and full step-by-step worked solutions. Students will build confidence calculating gradients from two points. They will also write line equations and analyze parallel, perpendicular, and intersecting lines. ________________________________________ Bring clarity to coordinate geometry with this no-prep linear graphs worksheet bundle. Designed for secondary maths students. It is fully optimized for UK National Curriculum Key Stage 3, Key Stage 4, and GCSE Maths preparation. This resource breaks down coordinate geometry into scaffolded skills. Every problem comes with a complete, line-by-line worked solution key. It is an excellent resource for independent classwork, homework, cover lessons, or exam revision. **What’s Included in This Bundle?** • **Part 1: Finding Gradient from Two Points** o 24 structured problems using the gradient formula. o Includes positive, negative, zero, and undefined gradients. • **Part 2: Writing the Equation of a Line (y = mx + c)** o 20 targeted problems finding the equation of a line. o Given a specific gradient m and a passing point A. o Practice ranges from basic origin points (0,0) to fractional gradients. • **Part 3: Parallel, Perpendicular, Intersecting, & Coinciding Lines** o Comprehensive review of linear graphs and their relative positions. o Analysis tasks proving whether lines are parallel, perpendicular, or intersecting. o Challenge problems writing equations parallel or perpendicular through given points. • **Complete Step-by-Step Solutions** o Full, line-by-line worked solutions for every single question. o Perfect for quick teacher grading or student self-checking. **Why Teachers Love This Resource:** • Ready-to-Print Printables: Just print and hand out. No extra preparation required. • Scaffolded Progress: Skills move logically from single gradients to full equations. • GCSE Aligned: Focuses directly on standard notation and the perpendicular gradient rule (m1 * m2 = -1). ________________________________________

£3.35
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Equation of a line (various cases) worksheets (with solutions)

A collection of four worksheets on determining the equation of a line in the following cases: given its gradient and a point on it, given point and a line to which is parallel, given a point on it and a line to which is perpendicular and given two points on it. Detailed solutions are included.

£3.75
Bundle

Equation of a line given its gradient and a point worksheets (with solutions)

A collection of three worksheets on determining the equation of a straight line given its gradient and a point on it. Solutions are provided.

£2.80

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