Understanding Line Gradients and Slopes

The video tutorial explains the concept of gradient, a measure of line steepness, and demonstrates how to calculate it using three methods: rise over run, change in y over change in x, and a simple rise per unit run. It uses examples of hills and graphs to illustrate positive, zero, and negative gradients. The tutorial also covers using equations for gradient calculation and concludes with a summary of key points.

What does the term 'gradient' primarily measure in a line?

• The width of the line

• The steepness of the line

• The length of the line

• The color of the line

Which hill has the highest gradient?

• The one that slopes downwards

• The one that is less steep

• The one that is completely flat

• The one that increases in height most quickly

How is the gradient of a line calculated using the rise over run method?

• By dividing the rise by the run

• By adding the rise and run

• By multiplying the rise and run

• By dividing the run by the rise

If a line goes up by 0.5 for every unit it goes across, what is its gradient?

• 0.5

• 1

• 2

• 0

Which equation can be used to calculate the gradient of a line?

• Gradient = rise + run

• Gradient = rise / run

• Gradient = rise * run

• Gradient = run / rise

What is the gradient of a line that does not rise at all?

• Zero

• Negative

• Positive

• Undefined

What is the change in y if a line goes from y = -1 to y = 2?

• 4

• 3

• 2

• 1

When a line slopes downwards, what type of gradient does it have?

• Positive

• Zero

• Negative

• Undefined

How do you determine the gradient of a line that slopes downwards more steeply?

• It becomes zero

• It becomes more negative

• It becomes more positive

• It remains the same

What is the gradient of a line that goes down from 3 to -3 on the y-axis?

• -1

• -6

• -2

• -3