Understanding Gradients from Graphs

In this video, Lucy explains how to find the gradient of a straight line from a graph. The gradient indicates the steepness of a line, with positive gradients going in one direction and negative in the opposite. She discusses real-world applications, such as fuel consumption and currency conversion. Lucy demonstrates how to calculate the gradient using two exact points on a line, forming a triangle to determine the rise and run. A practice problem is provided to reinforce learning. The video concludes with a preview of finding the equation of a line in the next video.

What does the gradient of a line represent in a distance-time graph?

• The acceleration

• The speed

• The time taken

• The distance traveled

Which of the following is NOT a real-world application of straight line graphs?

• Currency conversion

• Fuel consumption comparison

• Weather forecasting

• Data comparison

Which of the following is true about a line with a positive gradient?

• It slopes downwards from left to right

• It is horizontal

• It slopes upwards from left to right

• It is vertical

How do you determine the gradient of a line using two points?

• Add the y-coordinates

• Divide the change in y by the change in x

• Multiply the x-coordinates

• Divide the change in x by the change in y

If a line has a gradient of 3/2, what does this mean?

• For every 3 units along, it goes 2 units up

• For every 3 units up, it goes 2 units along

• For every 2 units up, it goes 3 units along

• For every 2 units along, it goes 3 units down

What is the formula for calculating the gradient of a line?

• Run over rise

• Change in x over change in y

• Rise over run

• Sum of x and y

What is the gradient of a line if the rise is 6 and the run is 3?

• 0.5

• 1

• 3

• 2

Why is the gradient negative in the practice problem?

• Because the line is horizontal

• Because the line slopes upwards

• Because the line slopes downwards

• Because the line is vertical

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

• The line is vertical

• The line is moving upwards

• The line is moving downwards

• The line is horizontal

What is the next topic to be covered in the following video?

• Finding the gradient of a curve

• Finding the equation of a line

• Understanding horizontal lines

• Calculating the area under a curve