Coordinates and Graphs
4.0 Geometry · 4.2 Coordinates and Graphs
Syllabus tag: Kenya CBC | Grade 8 Mathematics | Strand 4.0 Geometry | Sub-Strand 4.2 Coordinates and Graphs (14 lessons)
Lesson objectives
By the end of this sub-strand, you should be able to:
- Draw a labelled Cartesian plane and plot points on it
- Generate a table of values for a linear equation and draw its graph
- Solve simultaneous linear equations graphically
Coordinates and Graphs
Two numbers fix a point on a map, and two numbers fix a point on a graph. Once you can plot points you can draw a line. Once you can draw two lines you can solve equations by looking.
a) The Cartesian plane
Two number lines crossing at right angles make a Cartesian plane. The across line is the x-axis, the up line is the y-axis, and they meet at the origin.
A point is written as a pair, x first and y second. So (3, 2) means three across and two up.
The order matters. (3, 2) and (2, 3) are different points.
The axes cut the plane into four quadrants, numbered anticlockwise from the top right.
b) A table of values
To draw the graph of an equation, first work out some points.
Choose three values of x, not two. Two points always make a line, even if one is wrong. The third point catches the mistake, because it will not sit on the same line.
c) Drawing the graph
Plot each point carefully, then join them with a ruler. Extend the line past the points you plotted.
If the three points do not lie in a straight line, check the table before drawing.
d) Solving two equations by graph
Two linear equations can be solved by drawing both lines on the same plane.
The lines drawn are y = 2x and y = 6 − x. Where they cross, both equations are true at once, and that crossing point is the solution.
Read the coordinates of the crossing point. Here the lines meet at (2, 4), so x is 2 and y is 4.
e) Checking the answer
Substitute your values back into both original equations. If both are satisfied, the answer is right.
A graphical solution is only as accurate as the drawing. Use a sharp pencil, a ruler, and a sensible scale, and read the crossing point carefully.
If the two lines are parallel they never cross, and there is no solution.
f) Where this is used
A shopkeeper comparing two pricing offers finds where they cost the same. An engineer reads where two measurements match. Any question asking when two changing quantities become equal is this idea.
Words to know
- Cartesian plane -- a grid formed by a horizontal x-axis and vertical y-axis, used to locate points by coordinates.
- Coordinate pair -- a pair of values (x, y) that locates a specific point on the Cartesian plane.
- Table of values -- a list of (x, y) pairs generated by substituting chosen x-values into an equation.
:::checkpoint Check yourself
- Which quadrant contains the point (−3, 4)?
- Complete a table of values for y = 3x − 1 when x is 0, 1 and 2.
- What does the crossing point of two lines tell you?
- Why should you plot three points rather than two? :::
Bridge to practice
Try the exercises below -- on plotting points, generating tables of values, and solving simultaneous equations graphically.