A worksheet on identifying the equation of a line that passes through the origin (0,0), given its graph. The students have to spot a point on the line and substitute the coordinates of this point on the equation y=ax in order to find the value of the parameter a.
Detailed solutions are included.

Are your students learning how to write the equations of straight lines from a graph for the very first time? This clean, highly focused practice worksheet is the perfect introductory tool! By focusing exclusively on straight lines that pass through the origin (0,0), this resource eliminates the confusion of the y-intercept, allowing students to completely master calculating the gradient and understanding direct proportion.

Whether you are teaching proportional relationships at Key Stage 3 or introducing linear graphs ($y = mx + c$) at GCSE, this 12-problem worksheet provides the targeted, scaffolded practice your classes need to succeed.

What’s Included in This Resource?

• 12 Graphing Problems: Students are given a coordinate grid featuring a linear graph passing through the origin and must determine its exact equation.
• Varied Difficulty Levels: Includes a healthy mix of positive gradients, negative gradients, and fractional gradients to truly test student comprehension.
• Special Case Included: Features the zero-gradient horizontal special case ($y = 0$) to challenge higher-order thinking.
• Step-by-Step Solutions Sheet: A full, comprehensive answer page that models exactly how to substitute a coordinate point into the equation to algebraically solve for the gradient. Perfect for fast marking or student self-assessment!

Why Teachers Love This Resource:

• Zero Prep Required: Just print and go! Ideal for independent practice, homework assignments, a quick low-stakes quiz, or cover work.
• Clutter-Free Visuals: The clear, high-quality grid layouts make it easy for students to identify exact coordinate points without getting overwhelmed.
• Perfect for Differentiation: Excellent as a “Day 1” introduction to linear graphs, or as a remediation tool for students who need a refresher on gradients.

Curriculum Mapping & Exam Standards:

• Key Stage 3 National Curriculum: Move from introductory proportional relationships to recognizing, sketching, and producing graphs of linear functions.
• GCSE Maths (Foundation & Higher): Work with coordinates and graphs in all four quadrants; find equations of straight lines in the form $y = mx + c$ (where $c = 0$); interpret the gradient of a straight-line graph.