Understanding Linear Functions and Gradients

The video tutorial explains the linear equation y=mx+b, focusing on the roles of m (gradient) and b (y-intercept). It demonstrates how changing m affects the slope of the line and how b shifts the line vertically. The tutorial also covers calculating the gradient using the rise over run method and relates these concepts to a table of values, showing how changes in m and b impact the graph's appearance.

What does the 'm' in the equation y = mx + b represent?

• The constant term

• The x-intercept

• The slope or gradient

• The y-intercept

How does increasing the gradient 'm' from 1 to 2 affect the line on a graph?

• The line shifts downwards

• The line becomes more steep

• The line becomes less steep

• The line shifts upwards

What is the formula used to calculate the gradient of a line?

• Rise over run

• Difference of x and y

• Sum of x and y

• Run over rise

If a line has a rise of 8 and a run of 4, what is its gradient?

• 8

• 4

• 2

• 1

Why is it important to choose clear points when calculating the gradient?

• To change the slope of the line

• To ensure the line is straight

• To avoid errors in reading values

• To make the graph look better

What happens to the y-values in the table when the gradient is increased?

• They decrease

• They become negative

• They remain constant

• They increase by the gradient value

How does a negative gradient affect the line on a graph?

• The line falls

• The line rises

• The line becomes horizontal

• The line becomes vertical

What effect does changing the y-intercept 'b' have on the graph?

• It shifts the line vertically

• It changes the slope

• It rotates the line

• It changes the x-intercept

If the y-intercept is increased, what happens to the line?

• It moves down

• It moves up

• It becomes steeper

• It becomes less steep

Which component of the equation y = mx + b affects the steepness of the line?

• The y-intercept 'b'

• The gradient 'm'

• The x-value

• The constant term