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13 Jan 2026

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2 pages

Understanding Graphs in Mathematics

B€LA〄

@bxla

Graphs are everywhere in maths and real life - from... Show more

Year 10 Foundation Topic 4 Graphs Student Knowledge Organiser

Key words and definitions

Graph - A diagram showing the relationship between

Graph Fundamentals and Line Equations

Understanding graphs starts with knowing that they show relationships between two variables plotted on axes. Think of it like a visual way to see how one thing affects another - brilliant for spotting patterns quickly!

The equation of a straight line follows the format y = mx + c, where m is the gradient (how steep the line is) and c is the y-intercept $where the line crosses the y-axis$ . To find any line's equation, simply work out the gradient first, then spot where it hits the y-axis.

Parallel lines have identical gradients but different y-intercepts, whilst perpendicular lines meet at right angles. When drawing graphs, you'll complete a table of values by substituting x-values into your equation, then plot these coordinate points and join them with a straight line.

Quick Tip: Always double-check your plotted points - one wrong coordinate can throw off your entire line!

Distance Formulas and Real-Life Applications

Finding the midpoint between two points is dead simple - just find the average of the x-coordinates and the average of the y-coordinates. The formula looks scary, but it's basically finding the mean twice!

The distance formula uses Pythagoras' theorem to calculate how far apart two points are. You're creating a right-angled triangle and finding the hypotenuse length - perfect for working out actual distances on coordinate grids.

Distance-time graphs bring maths into the real world by showing journeys. The gradient tells you the speed $steeper = faster$ , flat sections show stops, and you can read off distances and times directly from the axes. These graphs are brilliant for analysing everything from car journeys to delivery routes.

Remember: On distance-time graphs, a steeper line means higher speed - horizontal lines mean you've stopped completely!

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Maths

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492

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13 Jan 2026

•

2 pages

Understanding Graphs in Mathematics

B€LA〄

@bxla

Graphs are everywhere in maths and real life - from tracking your phone battery to plotting journeys on maps. This topic covers everything you need to master straight line graphs, from writing equations to interpreting distance-time graphs that show real-world... Show more

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Graph Fundamentals and Line Equations

Quick Tip: Always double-check your plotted points - one wrong coordinate can throw off your entire line!

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Distance Formulas and Real-Life Applications

Remember: On distance-time graphs, a steeper line means higher speed - horizontal lines mean you've stopped completely!