1. Starter Questions
Factorise 5x + 10

2. The Straight Line Equation
Learning Intention
To explain and draw straight lines of the form y = mx + c.

3. The Straight Line Equation
By calculating the gradient of each line, write down the equation of the line y
The Straight Line Equation 1 2 4 3 5 x

4. The Straight Line Equation
Gradient = vertical height
horizontal distance
= 4 1
= 4
Equation of line is y = 4x
Line 2
Gradient = vertical height
horizontal distance
= 3 2
Equation of line is y = 3x 2
Line 3
Gradient = vertical height
horizontal distance
= 2 2
= 1
Equation of line is y = x

5. The Straight Line Equation
Gradient = vertical height
horizontal distance
= 1 2
Equation of line is y = 1x 2
Gradient = vertical height
horizontal distance
= 1 4
Line 5
Equation of line is y = 1x 4

6. The Straight Line Equation
All the lines we have previously looked at
all passed through the origin at (0,0)
i.e. y = 2x, y = 3x, y = ½x, y = 5x etc…
Gradient = 3
Gradient = 5
Gradient = 2
Gradient = ½
What about straight lines that do not pass through the origin

7. The Straight Line Equation
Example
Draw the line of y = 2x on a suitable coordinate diagram
y = 2x + 2 y x
Same gradient, but slightly higher up y 2 4 6 8
y = 2x
On the same diagram, draw the graph of y = 2x + 2 x y
2(0)+2
2(0)+2
2(0)+2
2(3)+2
2(4)+2 =2 =4 =6 =8
=10 x
What do you notice about the second line?

8. The Straight Line Equation
Example
Draw the line of y = x on a suitable coordinate diagram y x
y = x + 4
Same gradient, but slightly higher up y 1 2 3 4
y = x
On the same diagram, draw the graph of y = x + 4 x y 4 5 6 7 8 x
What do you notice about the second line?

9. The Straight Line Equation
y = x
On your 4 quadrant diagram, Draw the lines of the given equations.
The Straight Line Equation 1 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -2 -1
-10 x y x y 2 4
y = 3x+1 2 4 x y 1 2 1 4 7
y = x - 3
y = 2x + 3 x y 4 8 x y 1 2 -3 1 5 3 5 7

10. Straight Line Equationy 10
lines are parallel if they have the same gradient
All straight lines have
the equation of the form 9 8
y = mx + c 7 6 5 4 3
Where line
meets y-axis 2
Gradient 1 x 1 2 3 4 5 6 7 8 9 10
Find the equations of the following lines
y = x
y = x+4
y = 4x+2
y = -0.5x+2

11. Straight Line Equation
Now try Ex 4
Ch6 Page 73
Start at Q4