Tales by Dots and Lines

Overview

This chapter introduces the coordinate plane, plotting points, and reading and drawing line graphs. Dots (points) and lines tell stories about how quantities change, which is the start of graphical data handling.

Key concepts

• A point is located by an ordered pair (x, y): x along the horizontal axis, y along the vertical.
• The two axes meet at the origin (0, 0).
• A line graph joins points to show a trend over time.
• A graph through the origin that is a straight line shows direct proportion.

Important formulae

• Coordinates are written as (x-coordinate, y-coordinate).
• Points on the x-axis have y = 0; points on the y-axis have x = 0.
• For y = kx, the graph is a straight line through the origin.

Solved example

1. Plot A(2, 3) and B(4, 6) and check if O, A, B are collinear.
2. For A, y ÷ x = 3 ÷ 2; for B, 6 ÷ 4 = 3 ÷ 2.
3. The ratios are equal, so O(0,0), A and B lie on one straight line.

Important questions

1. Plot the points (1, 1), (3, 3) and (5, 5) and describe the pattern.
2. Where do points with x-coordinate 0 lie?
3. Draw a line graph for a car covering 20, 40, 60 km in 1, 2, 3 hours.
4. Read off the distance at 2.5 hours from your graph.

Quick revision

Always write coordinates as (x, y) and plot x first. The origin is (0, 0). Line graphs reveal trends; a straight line through the origin means the two quantities are in direct proportion.