You can use an equation to find pairs of values of x and y that obey the rule.

Remember that an equation is like a rule connecting x and y.

All the graphs in this unit will be straight lines.

Look at the equation $y = x + 2$.
Choose any value for x and then work out the corresponding values of y. Each time you will get the coordinates of a point.
• If $x=4$ $ \to $ then $y = 4 + 2 = 6$ $ \to $ This gives the coordinates $(4,6)$.
• If $x=1$ $ \to $ then $y = 1 + 2 = 3$ $ \to $ This gives the coordinates $(1, 3)$.
• If $x=-3$ $ \to $ then $y=-3 + 2 = -1$ $ \to $ This gives the coordinates $(-3,-1)$.
• If $x=0$ $ \to $ then $y = 0 + 2 = 2$ $ \to $ This gives the coordinates $(0,2)$.
If you plot these points, you can draw a straight line through them.
Any other points you find, using this equation, will be on the same line, $y = x + 2$.

If your line is not straight, check you have worked out the coordinates correctly.

a: Complete this table of values for $y = 5 - 3x$.
b: Use your table to draw the graph of $y = 5 - 3x$.

3	2	0	1-	2-	x
1-	2-		8		y

3	2	0	1-	2-	x
4-	1-	5	8	11	y

If $x = - 2$ then $y = 5 - 3 \times - 2 = 11$
If $x = 0$ then $y = 5 - 3 \times 0 = 5$
If $x = 3$ then $y = 5 - 3 \times 3 = - 4$

It is always helpful to put the values in a table, like this.

Think carefully about the numbers you put on the axes.
The x-axis must include -2 and 3. The y-axis must include -4 and 11.
Make sure you can plot all five points.
The points are in a straight line. Draw a line through all the points.
Make the line as long as the grid allows.

1) a: Copy and complete this table of values for $y = x + 4$.

4	2	0	3-	5-	x
	6		1		y

b: Copy these axes. Use your table to draw the graph of $y = x + 4$.

2) a: Copy and complete this table of values for $y= 2x + 5$.

3	2	0	2-	4-	x
11			1		y

b: Copy these axes. Use your table to draw the graph of $y= 2x + 5$.

3) a: Complete this table of values for $y= x - 3$.

6	4	2	1-	2-	x
				5-	y

b: Use your table to draw the graph of $y = x - 3$.
c: Where does the graph cross the x-axis?

When you draw the coordinate grid, look carefully at the table of values so that you will know how to label the axes.

4) a: Complete this table of values for $y = 5 - x$.

6	5	2	1-	3-	x
	0		6		y

b: Use your table to draw the graph of $y= 5 - x$.
c: Where does the graph cross the x-axis?

5) a: Complete this table of values for $y = 2 - x$.

5	3	2	0	2-	4-	x
					5-	y

b: Draw the graph of $y = 2 - x$.

6) a: Complete this table of values for $y= 2(x + 1)$.

5	2	0	2-	4-	x
				6-	y

b: Draw the graph of $y=2(x+1)$.

7) a: Complete this table of values for $y= 3-2x$.

4	2	1	0	1-	2-	x
	1-				7	y

b: Draw the graph of $y=3-2x$.

8) a: Complete this table of values for $y=2x-4$.

5				3-	x
6					y

Choose your own values of x between -3 and 5.
b: Draw the graph of $y= 2x-4$.
c: Where does the graph cross each of the axes?

9) a: Draw the graph of $y=6-x$ with values of x from -2 to 7.
b: On the same axes draw the graph of $y= 2$.
c: Where do the two lines cross?

Summary

You should now know that:
* The x-axis is horizontal and the s-axis is vertical.
* The first coordinate is the x-coordinate and the second coordinate is the y-coordinate.
Coordinates can be positive, negative or zero.
* Straight lines on a coordinate grid have equations.
* Lines with equations of the type $x=2$ or $y=-3$ are parallel to the axis or x-axis respectively.
* An equation such as $y=2x-3$ can be used to work out coordinates and draw a straight-line graph.
You should be able to:
* Read and plot positive and negative coordinates of points determined by geometric information.
* Recognise straight-line graphs parallel to the xaxis and y-axis.
* Generate coordinate pairs that satisfy a linear equation, where y is given explicitly in terms of x, and plot the corresponding graphs.
* Draw accurate mathematical graphs.
* Recognise mathematical properties, patterns and relationships, generalising in simple cases.