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Equation of a straight line passing through two points worksheet (with solutions)

Equation of a straight line passing through two points worksheet (with solutions)

Subject: Mathematics

Age range: 14-16

Resource type: Worksheet/Activity

Last updated

1 August 2026

pdf, 79.14 KB
pdf, 79.14 KB

A worksheet on finding the equation of a straight line given two points on the line. Detailed solutions 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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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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Slope Intercept Form Worksheets | Finding Slope from Two Points | Algebra 1

Three worksheets on finding the gradient of a straight line passing through two given points, identifying the gradient and y-intercept of a straight line given it equation and finding the equation of a straight line given two points on the line. Detailed solutions are included. Master straight-line graphs, finding gradients, and equations of lines with this no-prep math worksheet bundle! It builds clear fluency in calculating gradients using coordinates, writing equations in the form y = mx + c, and rearranging linear expressions. Perfect for KS3 and KS4 math lessons, weekly homework tasks, or GCSE revision practice. ________________________________________ Looking for a print-and-go resource to help your students master straight-line graphs and coordinate geometry? This comprehensive worksheet bundle features a perfectly scaffolded algebraic progression designed to take students from basic gradient calculations to constructing full linear equations. With clean layouts and exhaustive problem sets, it makes differentiation and lesson planning completely effortless. This resource is fully aligned with the UK National Curriculum for Key Stage 3 (KS3) and Key Stage 4 (KS4) / GCSE Mathematics, specifically focusing on the equation of a straight line. 📌 **What's Included:** • **Finding Gradient from Two Points Worksheets:** Targeted practice using the gradient formula across positive, negative, and fractional coordinate pairs. • **Equations of Straight Lines Passing Through Two Points:** Clear layouts guiding students to calculate the gradient, use substitution to find the y-intercept, and write the complete equation. • **Isolating Gradient & Y-Intercept Worksheets:** Practice exercises requiring students to rearrange mixed or multi-step expressions directly into standard y = mx + c form. • **Complete Answer Keys:** Full, step-by-step worked solutions are provided for every single problem to ensure lightning-fast marking or independent student self-checking. 📝 **Perfect For:** • Independent classroom practice, structured classwork, or weekly homework tasks • Small group math intervention, numeracy remediation, and GCSE exam preparation • Fast finishers, targeted revision, and hassle-free emergency cover lesson plans ________________________________________

£2.80
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Slope & Writing Linear Equations Worksheet Bundle | Algebra 1

Seven worksheets on straight lines. Students are required to: * examine whether a point is on a straight line or not * identify the gradient and y-intercept of a given line given its equation * find the gradient of a line passing through two given points * find the equation of a line given its gradient and a point on it * find the equation of a line given two given points on it * determining whether two lines are parallel perpendicular or neither. * find gradients of straight lines, perpendicular lines and parallel lines * find the midpoint of a line segment Detailed solutions are provided. A comprehensive, no-prep bundle of 7 straight-line graphs worksheets. Covers finding gradients from two points, writing equations in \(y = mx + c\) form, midpoints, and parallel/perpendicular lines. Complete with full, worked step-by-step solutions. Ideal for KS3, KS4 GCSE Maths revision, homework, or cover lessons! ________________________________________ Master straight-line graphs and coordinate geometry with this complete, no-prep 7-worksheet resource bundle! Whether you are teaching linear graphs for the first time or prepping your GCSE students for their upcoming maths exams, this comprehensive bundle provides structured, targeted practice. Each of the 7 worksheets focuses on a foundational coordinate geometry skill, moving smoothly from core definitions to multi-step exam-style problem-solving. Best of all, complete, step-by-step worked solutions are included for every single question, making peer-marking, self-assessment, or teacher grading an absolute breeze! **Key Skills Covered:** • **Finding the Gradient:** Calculating the gradient from two coordinate points (covering positive, negative, zero, and fractional gradients). • **Identifying Key Attributes:** Rearranging linear equations into standard form (y = mx + c) to instantly identify the gradient and y-intercept. • **Writing Straight-Line Equations:** Determining the full equation of a line passing through two given coordinate points. • **Verifying Points:** 91ting coordinates algebraically to prove whether a specific point lies on a given line. • **Midpoint Formula:** Finding the exact middle coordinate of a line segment. • **Parallel & Perpendicular Lines:** Writing equations for lines that run parallel or perpendicular to a given equation while passing through a specific point. **Perfect For:** • KS3 Maths Extension & Core Learning • KS4 GCSE Maths Revision (Foundation and Higher tiers) • Independent Study, Homework Tasks, or Weekly Booklets • Low-stakes Assessment, Remediation, & Intervention Groups • High-quality, Print-and-Go Cover Lessons (No preparation required!) **What’s Included in Your Download?** • 7 Student Practice Worksheets (Clean layout with plenty of working-out space) • 7 Complete Teacher Answer Keys featuring fully worked-out, line-by-line solutions ________________________________________ **Love This Resource?** If you found these worksheets helpful, please leave a review to let other teachers know! Be sure to follow my TES shop to get notified as soon as new secondary maths bundles, freebies, and revision resources are uploaded. AI responses may include mistakes. Current limitations only allow part of the document to be used for this answer. Learn more

£3.90
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Coordinate Geometry Bundle: Midpoint, Gradient & Equation from Two Points

Three worksheets on the following: midpoint of a line segment, gradient of a straight line passing through two points and equation of a line passing through two points. Detailed solutions are included. Master coordinate geometry with this complete three-pack worksheet bundle. Perfect for Key Stage 3 (KS3) and GCSE Maths revision, these practice packs build total confidence in finding the midpoint of a line segment, calculating gradient, and finding the equation of a line from two points. Full teacher worked solutions are included! ________________________________________ Stop spending hours formatting coordinate geometry sheets. This comprehensive Coordinate Geometry Bundle: Midpoint, Gradient & Equation from Two Points is designed to build complete mastery. It moves students seamlessly from basic coordinate averaging to high-rigour linear calculations involving tricky negative integers and fractions. Perfect for introducing linear graphs at Key Stage 3 or as a comprehensive revision packet for Key Stage 4 GCSE Foundation and Higher tiers. **What is Included in this Pack?** • **Midpoint of a Line Segment Pack:** Clear, spacious layouts for calculating exact middle coordinates from positive and negative coordinate pairs, leading to decimal answers. • **Gradient of a Straight Line Pack:** Comprehensive practice using the gradient formula across vertical lines, horizontal zero-gradient planes, and negative fraction solutions. • **Equation from Two Points Exercises:** Step-by-step sheets for calculating gradient, substituting a coordinate point, and solving for the y-intercept constant to write complete straight-line equations in y = mx + c form. • **Detailed Step-by-Step Worked Solutions:** Comprehensive answer sheets showing every single stage of the calculation—perfect for cover work, busy teachers, or student self-assessment. **Key Skills & Concepts Covered** • **Coordinate Averaging:** Correctly utilizing midpoint formulas with direct negative number integration. • **Rise Over Run (Gradient):** Managing calculations for positive, negative, zero, and fractional slopes. • **Writing Straight-Line Equations:** Solving for the y-intercept constant (c) and assembling equations with complex non-integer fractions (e.g., y = -5/3x + 28/3). **Ideal For:** • Independent classroom practice worksheets or homework booklets. • Targeted GCSE Maths exam revision and diagnostic intervention. • Ready-made, no-prep cover lessons or math revision stations.

£3.40
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Equation of a line worksheets (with solutions)

A collection of 3 worksheets. Two worksheets on finding the equation of a line that passes through a given point and has a given slope and a worksheet on finding the equation of a line that passes through two given points. Detailed solutions are included.

£2.70
Bundle

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

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