Understanding Gradient and Slope

This 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. The video uses hill examples to illustrate different gradient values, including positive, zero, and negative gradients. It also covers how to apply these methods to graphs and equations, providing a comprehensive understanding of gradient calculation.

What does a gradient of zero indicate about a line?

• The line is vertical.

• The line is horizontal.

• The line is flat.

• The line is steep.

Which method involves measuring how much a line rises for each unit it moves across?

• Slope-intercept method

• Gradient-intercept method

• Rise over run method

• Point-slope method

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

• 0.5

• 1

• 2

• 0

What is the formula for calculating gradient using the rise and run?

• Gradient = run / rise

• Gradient = rise / run

• Gradient = change in x / change in y

• Gradient = x / y

How do you calculate the gradient between two points on a graph?

• By finding the difference in x-values

• By finding the difference in y-values

• By dividing the change in y by the change in x

• By adding the x and y values

What is the gradient if a line goes from y = -1 to y = 2 while x goes from -4 to 2?

• 3

• 1

• 2

• 0.5

What does a negative gradient indicate about the direction of a line?

• The line is horizontal.

• The line is sloping upwards.

• The line is sloping downwards.

• The line is vertical.

If a line goes down by 2 for every unit it moves across, what is its gradient?

• 2

• -1

• -2

• 0

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

• By measuring the rise over run

• By measuring the run over rise

• By finding the sum of x and y

• By finding the product of x and y

What is the gradient if a line goes from y = 3 to y = -3 while x goes from -1 to 2?

• -2

• -1

• -3

• -4