Functions
Introduction to graphs
Plot and read points on a grid, read a line graph, and work out values from a simple linear relation.
A graph turns numbers into a picture. Two axes cross at the origin: the x-axis goes across and the y-axis goes up. A point is written (x, y), always across first and up second, so (3, 5) and (5, 3) are two different places on the page.
Have a play
This graph follows one journey from start to finish, with time along the bottom and distance up the side. Find out what each stretch of the line says about it.
Tap any part of the picture.
What the shape of a line tells you
On a distance-time graph, a rising line means moving, a steeper line means moving faster, and a flat line means stopped — time still passes but the distance does not change. A relation like y = 2x + 1 draws a straight line too: pick two or three values of x, work out y for each, plot them, and join them up.
Worked example
Draw the graph of y = 2x by working out three points.
Take x = 0. Then y = 2 × 0 = 0, giving the point (0, 0).
Starting at zero is worth doing every time: it tells you straight away whether the line passes through the origin.
Try it together
Now let us find three points on the line y = 3x - 2 together.
Substitute a value of x, work out y, and write down the pair. Then do it again.
1.Put x = 1 into y = 3x - 2. What is y?
Have a go
Have a go on your own: for the relation y = 5x + 4, what is y when x is 3?
Hint: Multiply before you add.
Ready to practice?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.