Gradient of a Line (SQA National 5 Maths): Revision Note

Determining the gradient of a straight line between two points

What is the gradient of a line?

• The gradient is a measure of how steep a straight line is

• A gradient of 3 means:

  • For every 1 unit to the right, go up by 3

• A gradient of -4 means:

  • For every 1 unit to the right, go down by 4 

• A gradient of 3 is steeper than a gradient of 2

  • A gradient of -5 is steeper than a gradient of -4

• A positive gradient means the line goes upwards (uphill)

  • Bottom left to top right 

• A negative gradient means the line goes downwards (downhill)

  • Top left to bottom right

How do I find the gradient of a line?

• Find two points on the line and draw a right-angled triangle

  • Then

  • Or, in short,  

    • The rise is the vertical length of the triangle

    • The run is the horizontal length of the triangle

  • Put the correct sign on your answer

    • Positive for uphill lines

    • Negative for downhill lines

  • You can also find gradient of a line between two points,  and  

    • Use the formula 

How do I draw a line with a given gradient?

• To draw the gradient 

  • The rise is 2

  • The run is 3

  • It is positive (uphill)

    • Move 3 units to the right and 2 units up

• To draw the gradient  make it a fraction, 

  • The rise is 5

  • The run is 1

  • It is negative (downhill)

    • Move 1 unit to the right and 5 units down