Introducing: Straight Line Graphs
Hints and Tips
This activity is an opportunity for you to guide your child as he/she investigates straight lines drawn on the four quadrants.
In this topic your child will look at different lines, some of which will go through the origin, others will cut the x or y axis.
Here are some examples of lines for you to look at before you start working with your child.
Essential Prior Knowledge
how to draw and read coordinates in all 4 quadrants
how to use a ruler to accurately draw a straight line
to be able to find patterns and draw conclusions
Activity
Activity One
Using graph paper, appropriate to the ability of your child, ask him/her to draw and label axes that go across and down the paper giving both positive and negative numbers on each.
Ask your child to draw a vetrical line on the positive side of the axis, ensure that it goes from the top of the paper to the bottom, cutting the axis.
Ask your child to write down the coordinates of ten points on the line (this would be easiest if your child read them at points where they are whole numbers)
It is important your child records these in an organised way, as he/she will be looking for a pattern.
Ask your child what he/she notices about the coordinates (the x coordinate of all the chosen points is the same)
This is where the name of the line comes from in this instance it will be x = (the number of the x coordinates on the line)
Now ask your child to do the same again, placing a line in the following positions:
- a horizontal line in the positive area (y = the number of the y coordinate)
- a vertical line in the negative area (x = the number of the x coordinate)
- a horizontal line in the negative area (y = the number of the y coordinate)
- a diagonal line at 45° to the positive x axis passing through the origin (0,0) (y = x)
- a diagonal line perpendicular to the line above also passing through the origin (y = -x)
For each line ask your child to collect coordinates from points on the line and from these work out the name of each line.
Ask your child what he/she notices anything about any of the lines.
Ask your child to explain why a line where y = a number is always horizontal and x = a number is always vertical
Activity Two
Ask your child to draw the following line graphs.
y = 3x
y = 1/2x
y = -2x
y = - 1/2x
What happens to the line when the number multiplied by x gets higher?
What happens to the line when x is multiplied by a negative number?
Encourage your child to explain how he/she will work out where the lines go. Then ask him/her to draw them and label them
(Work out at least 3 sets of coordinates for each line before drawing them on the graph paper)