GCSE Maths · Straight-Line Graphs and Coordinates · Higher · Summary

GCSE Maths Straight-Line Graphs and Coordinates (Higher): summary and key words

Part of the GCSE Maths straight-line graphs and coordinates chapter (Higher). Chapter overview · Foundation version of this lesson · whole chapter on one page

Chapter summary

Skill	Method
Coordinates	(x, y): across first, then up or down. Quadrants 1 to 4 go anticlockwise from the top right.
Midpoint	Add the coordinates and halve: ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2)
Length of a line segment	Subtract to find across and up, then Pythagoras: length² = across² + up²
Horizontal and vertical lines	y = b is horizontal; x = a is vertical
Drawing a line	Table of values, plot, ruler; or use c and the gradient; or the axis intercepts
Gradient	rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁)
y = mx + c	m is the gradient, c is the y-intercept; rearrange first if needed
Equation from two points	Find m, substitute a point to find c, check with the other point
Parallel lines	Equal gradients
Perpendicular lines (Higher)	Gradients multiply to −1 (negative reciprocal)
Real-life graphs	Gradient = rate of change; y-intercept = starting value; through the origin = direct proportion
Intersections	Read from the graph and check in both equations; Higher: set the right-hand sides equal and solve

I can read and plot coordinates in all four quadrants and find missing corners of shapes.
I can find the midpoint of a line segment, and (Higher) find an end point from the midpoint.
I can find the length of a line segment using Pythagoras’ theorem.
I can write the equations of horizontal and vertical lines.
I can draw a straight-line graph from a table of values.
I can find a gradient from a graph or from two points.
I can use y = mx + c to find the gradient and intercept and to sketch a line.
I can find the equation of a line from a graph, from two points or from a point and a gradient.
I can use gradients to decide if lines are parallel (and, Higher, perpendicular).
I can interpret the gradient and intercept of a real-life graph, and use a graph to find values.
I can find the point where two lines cross.

Coordinates: A pair of numbers (x, y) that gives the position of a point: across first, then up or down.
Origin: The point (0, 0) where the axes cross.
Quadrant: One of the four regions the axes divide the grid into.
Midpoint: The point exactly halfway between two points.
Line segment: The part of a straight line between two points.
Gradient: How steep a line is: rise ÷ run.
Rate of change: How much one quantity changes for each 1 unit of another; the gradient of a real-life graph.
y-intercept: The value of y where a line crosses the y-axis (where x = 0).
Linear: Giving a straight-line graph; x appears only to the power 1.
Parallel: Lines that never meet because they have the same gradient.
Perpendicular: Meeting at a right angle (90°); the gradients multiply to −1.
Point of intersection: The point where two lines cross.
Direct proportion: A relationship where doubling one quantity doubles the other; its graph is a straight line through the origin.
Bisect: To cut exactly in half.
Hypotenuse: The longest side of a right-angled triangle, opposite the right angle.