Coordinates and Graphs
Algebra · Coordinates and Graphs
Syllabus tag: KCSE | Mathematics | Form 1 | Topic 19 Coordinates and Graphs
Lesson objectives
By the end of this topic, you should be able to:
- Locate and plot points on the Cartesian plane.
- Choose and use an appropriate scale for given data.
- Make a table of values and draw the graph of a linear equation.
- Read and interpret information from graphs.
Coordinates and Graphs
The Cartesian plane fixes any point with two numbers, and turns an equation into a picture.
a) The plane
Two perpendicular number lines meet at the origin.
The horizontal is the x-axis; the vertical is the y-axis.
A point is written (x, y), across first and up second. The order matters: (3, 2) and (2, 3) are different points.
b) The quadrants
The axes divide the plane into four quadrants, numbered anticlockwise from the top right.
| Quadrant | x | y |
|---|---|---|
| First | + | + |
| Second | − | + |
| Third | − | − |
| Fourth | + | − |
The signs alone tell you which quadrant a point lies in.
c) Choosing a scale
Look at the range of values before drawing any axes.
Choose a scale that fits the paper and is easy to read. Try 1 cm to 1 unit, or to 2, 5 or 10 units.
Use the same scale on both axes when shape matters, such as when judging whether lines are perpendicular.
Label both axes and mark the scale.
d) A table of values
Choose at least three values of x, not two.
Two points always make a straight line, even if one is wrong. The third catches the error, because it will not lie on the same line.
Substitute each value carefully, watching the signs.
e) Drawing the graph
Plot each point, then join them with a ruler.
Extend the line a little past the plotted points.
Label the line with its equation.
If the points do not lie in a straight line, check the table before drawing anything.
f) Reading from a graph
To find y for a given x, go up from the x-axis to the line. Then go across to the y-axis.
To find x for a given y, go across then down.
Where the line crosses the y-axis is the y-intercept. Where it crosses the x-axis, y is zero.
Read to the nearest sensible division. Answers from a graph are approximate, and a question usually accepts a small tolerance.
g) Where this is used
Any relationship between two changing quantities. Distance-time graphs. Cost against quantity. Converting between currencies or units by graph.
Words to know
- Cartesian plane -- the plane formed by two perpendicular axes.
- Origin -- the point (0, 0) where the axes cross.
- Ordered pair -- coordinates written (x, y), with order significant.
- Quadrant -- one of the four regions into which the axes divide the plane.
- Interpolation -- reading a value within the range of plotted data.
:::checkpoint Check yourself
- In which quadrant does (−2, 5) lie?
- Make a table of values for y = 3x + 2 using x = 0, 1 and 2.
- Why plot three points rather than two?
- What is the y-intercept of a graph? :::
Bridge to practice
The exercises begin with plotting and quadrants, move through scales and tables of values, and finish with drawing lines, reading values and graphical solutions. Before drawing any graph, decide your scale and write it down; before joining points, check that all three lie in line.