Discover Mathematics P6: Term 1, Unit 5, Lessons 3–4
GoalRead values from a graph, find the equation and predict a value.
New words
read a value · go from one axis to the point and across to the other axispredict · use the pattern or equation to find a value that is not on the graphrepresent · show the same relationship in a different way
Explanation
A graph answers questions. To find the output for an input, start at the input on the x-axis, go up to the point, then go across to the y-axis. To find the input for an output, start on the y-axis and go across to the point, then down to the x-axis. To find the equation, read some points and ask how y changes when x goes up by 1: if the points are (1, 5), (2, 10), (3, 15), then y = 5x. The same relationship can be given in words, in a table, as an equation or as a graph, and we can move between them. We can predict a value that is not on the graph with the equation.
Form
Example
Words
5 LE for every kilogram
Table
x: 1, 2, 3 → y: 5, 10, 15
Equation
y = 5x
Graph
points (1, 5), (2, 10), (3, 15)
Worked examples
A cyclist’s graph shows d = 15t. After 2 hours the point is at 30 km. For 45 km, go across from 45 to the line and down: t = 3 hours.
The points (1, 6), (2, 12), (3, 18), (4, 24) are packs of 6 pencils. Each pack adds 6, so y = 6x. The next point would be (5, 30). We do not join the points because only whole packs are sold.
Ride tickets cost 12 LE each. The point (3, 36) means 3 tickets cost 36 LE. The equation is c = 12n, so 6 tickets cost 72 LE even though 6 is off the graph.
Class activity
Graph questions. Make a graph with a grown-up for a story you choose, such as water flowing from a tap. Ask each other three questions that can be answered by reading the graph: one that starts from x, one that starts from y, and one that needs the equation to predict.
Practice
1
Look at the graph of a cyclist: how far has the cyclist gone after 2 hours?
40 km.
2
In the same graph, how many hours does it take to travel 60 km?
3 hours.
3
Write the equation for the graph.
d = 20t, because d goes up by 20 for each hour.
4
If the pattern continues, what does the point (5, 100) mean?
After 5 hours the distance is 100 km (20 × 5).
5
Why should we not join the points of a graph of tickets sold?
We cannot sell 2.5 tickets, so the amounts in between do not make sense.
