Calculating Gradients

Gradient is the steepness or slope of a line. We've already learnt how to calculate gradient but let's just refresh ourselves on a couple of key points to start.

Other handy points to remember:

• The gradient formula can be thought of generally as:  $\text{Gradient }=\frac{\text{rise }}{\text{run }}$Gradient =rise run ​
• Gradient of Vertical Line is undefined
• Gradient of Horizontal Line $\text{= 0}$= 0

Even though we are used to finding the gradient of a line from two given pairs of coordinates, we may also need to reverse the process. Sometimes, we may be asked to find a pair of coordinates when we're given the gradient and a point.

Check out the examples to see the different ways we can work with the gradient formula.

Examples

Question 1

Consider the following ramp:

a) What is the gradient of this skateboard ramp if it measures $0.9$0.9 metres high and $1$1 metre across?

Think: What is the rise and run of this ramp?

Do: 

$\text{Gradient }$Gradient	$=$=	$\frac{\text{Rise }}{\text{Run }}$Rise Run ​
	$=$=	$\frac{0.9}{1}$0.91​
	$=$=	$0.9$0.9

 

b) It can only be used as a 'beginner’s ramp' if for every $1$1 metre horizontal run, it has a rise of at most $0.4$0.4 metres. Can it be used as a 'beginner’s ramp'?

Think: What is the maximum gradient of a beginners' ramp? Is the ramp steeper than this?

Do: A beginner's ramp needs to have a gradient of $\frac{0.4}{1}$0.41​ or $0.4$0.4. Since the ramp has a steeper gradient of $0.9$0.9, it cannot be used as a beginners' ramp.

 

Question 2