Introduction to Linear Equations (Graphing & Intercepts) Worksheet + Keys

Graphing Linear Equations: Slopes and Intercepts Worksheets (GCSE / KS4)

Three worksheets on linear equations. The exercises require to: * examine whether a given point is on a line * find points on a line * sketch the graph of a line * find a or b in y=ax+b given a point on the line * find the x-intercept and y-intercept of a line * find the equation of a line given its y-intercept and another point * find the intercepts of a line, points on a line and the equation of a line given its graph * find the slope of a line given its graph * find the slope of a line given two points on it * find the equations of vertical and horizontal lines given their graphs * sketch vertical and horizontal lines given their equations * find points on vertical and horizontal lines Detailed solutions to all worksheets are included. Master graphing straight lines, finding gradients, and calculating axes intercepts with this comprehensive, **no-prep, print-and-go** worksheet pack. Designed specifically for **GCSE (AQA, Edexcel, OCR) and Key Stage 4 (KS4)** students, this resource builds algebraic confidence through clean, easy-to-read layout templates. Whether you need emergency cover lessons, independent homework, scaffolded classwork, or targeted revision sessions before exam day, these worksheets give your students the exact practice they need to succeed with coordinate geometry. **What’s Included in This Worksheet Pack?** This downloadable resource contains three core coordinate geometry topics, complete with fully worked-out teacher answer keys: **1. Linear Equations & Coordinates Foundations** * Testing coordinate pairs (x, y) algebraically to determine if they lie on a given line. * Substituting values into linear functions to calculate and map unique coordinate points. **2. Finding the Gradient of a Straight Line** * Tracking the "Rise over Run" visually using clear, precise coordinate grids. * Using the algebraic gradient formula m = (y2 - y1) / (x2 - x1) across pairs of positive and negative integer points. * **3.Graphing Linear Lines & Intercepts** * Plotting and sketching straight lines using the standard y = mx + c format. * Rearranging linear equations to quickly solve for both x-intercepts and y-intercepts. * Dedicated practice for sketching Horizontal (y = c) and Vertical (x = c) lines, including identifying their common points of intersection. **Why Secondary Maths Teachers Love This Resource:** * Zero Prep Required: Simply download, print, and distribute directly to your classes. Perfect for stress-free lesson planning. * **Full Step-by-Step Answer Keys:** Every single question includes the complete algebraic working out—not just the final answers—making it ideal for quick teacher marking or student self-assessment. * **Clutter-Free Layout:** * Large, clean Cartesian coordinate grid planes give students plenty of physical space to plot points, draw straight lines, and show their calculations neatly. * **Versatile Use:** Excellent for initial secondary skill instruction, mid-topic intervention, homework assignments, or structured GCSE maths revision. * **Target Audience & Curriculum Fit**: * **Key Stages:** Key Stage 3 (KS3 Extension) & Key Stage 4 (KS4 / GCSE Foundation & Higher) * **Exam Boards**: Fully aligned with AQA, Edexcel, and OCR GCSE Maths specifications. * **Core Topics:** Linear graphs, straight-line equations, gradients, y-intercept, x-intercept, coordinates grid, plotting functions.