Discover Mathematics P6: Term 1, Unit 5, Lessons 3–4
GoalPlot ordered pairs in the first quadrant and decide whether to join the points.
New words
axis · a number line that frames the graph: x across, y upscale · the equal steps of the numbers on an axisplot · mark a point at its ordered pair
Explanation
To draw a graph of a relationship, use the first quadrant. The independent variable (input) goes on the horizontal x-axis and the dependent variable (output) on the vertical y-axis. Label each axis with its name and unit, and choose an even scale that is big enough for the largest number. Plot each ordered pair as a point: go across x, then up y. If every amount in between makes sense, like any time or any distance, join the points with a line. If only whole items make sense, like tickets, do not join them. Do not extend the line to the left of 0.
★Remember
Independent variable on the x-axis. Even scales. Label the axes. Join the points only if every amount in between makes sense.
Worked examples
A car travels d = 60t km. The points are (0, 0), (1, 60), (2, 120), (3, 180). Time can be any amount, such as 1.5 hours, so we join the points with a line.
Tickets cost 15 LE each: p = 15n. The points are (1, 15), (2, 30), (3, 45), (4, 60). You cannot buy 2.5 tickets, so we do not join the points.
A tank fills with water, rising 3 cm each minute: h = 3m. The points are (0, 0), (1, 3), (2, 6), (3, 9), (4, 12). Water rises smoothly, so we join them.
Class activity
Graph paper walk. Draw a big grid on the floor with chalk, 6 squares across and 6 up. Choose y = 2x. Walk across x and then up to y for x = 1, 2, 3, 4 and put a pebble at each point. Do the pebbles lie in a straight line? Write down the ordered pairs.
Practice
1
Which axis shows the independent variable?
The horizontal x-axis.
2
What are the coordinates of point A?
(3, 12): across 3 and up 12.
3
Notebooks are bought one at a time. Should we join the points of a graph of the number of notebooks and the cost?
No. Only whole notebooks make sense, so we plot separate points.
4
A table has x = 1, 2, 3 and y = 5, 10, 15. Write the points to plot.
(1, 5), (2, 10) and (3, 15).
5
Why must the scale on an axis be even?
Equal steps must mean equal amounts, otherwise the graph is stretched and gives a wrong picture.
