Understanding Gradients and Intercepts

The video tutorial covers graphing linear equations, focusing on identifying and plotting the y-intercept and gradient. The instructor demonstrates two examples: one with a positive gradient and another with a negative gradient, highlighting the differences in graph direction. The tutorial emphasizes the importance of setting up axes correctly and understanding the impact of positive and negative gradients on the graph's slope.

What is the first step you should take when drawing a graph?

• Calculate the gradient

• Mark the origin and axes

• Draw the line

• Plot the points

In the equation y = mx + b, what does 'b' represent?

• The gradient

• The y-intercept

• The x-intercept

• The slope

How do you determine the rise in the 'rise over run' method?

• By finding the y-intercept

• By measuring the horizontal distance

• By calculating the slope

• By counting the units up or down

What should you do after plotting the points on the graph?

• Erase the points

• Join the points with a line

• Calculate the gradient

• Find the y-intercept

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

• The line goes downwards

• The line is horizontal

• The line is vertical

• The line goes upwards

When modifying the equation to have a negative gradient, what remains unchanged?

• The y-intercept

• The direction of the line

• The x-intercept

• The gradient

What happens to the line when the rise is negative?

• It becomes horizontal

• It moves downwards

• It remains unchanged

• It moves upwards

How does a positive gradient affect the position of the line?

• The line moves downwards

• The line becomes horizontal

• The line becomes vertical

• The line moves upwards

What is the effect of a negative y-intercept on the graph?

• The line starts above the origin

• The line starts below the origin

• The line is vertical

• The line is horizontal

What is the significance of the x-intercept in a graph?

• It indicates the direction of the line

• It shows where the line crosses the y-axis

• It shows where the line crosses the x-axis

• It determines the slope of the line