GRADIENT

• What does the term gradient refer to in mathematics?


  It is a measure of how steep a particular line is.
• How can the gradient be calculated from a graph?


  By using three different methods: rise over run, change in y over change in x, and measuring the rise for each unit across.
• What is the gradient of a line that rises by 1 for every 1 it goes across?


  The gradient is 1.
• What does a gradient of zero indicate about a line?


  It indicates that the line is completely flat and not rising or falling.
• How does the steepness of a line relate to its gradient?


  A steeper line has a higher gradient, while a less steep line has a lower gradient.
• What is the equation for calculating the gradient?


  The gradient is equal to the rise divided by the run.
• How can the rise and run be defined in the context of a graph?


  The rise is how much the line has gone up, and the run is how much the line has gone across.
• If a line rises by 0.5 and runs by 1, what is the gradient?


  The gradient is 0.5.
• How do you find the gradient between two points on a graph?


  By calculating the rise over run between the two points.
• What is the change in x if you move from \( x = -4 \) to \( x = 2 \)?


  The change in x is 6.
• What is the change in y if you move from \( y = -1 \) to \( y = 2 \)?


  The change in y is 3.
• If the rise is 3 and the run is 6, what is the gradient?


  The gradient is \( \frac{3}{6} = 0.5 \).
• What does a negative gradient indicate about a line?


  It indicates that the line is sloping downwards.
• If a line goes down by 2 for every 1 it goes across, what is the gradient?


  The gradient is -2.
• How do you calculate the gradient using two points on a line?


  By finding the rise and run between the two points and calculating rise over run.
• What is the change in y if a line goes from 3 to -3?


  The change in y is -6.
• What is the change in x if a line goes from -1 to 2?


  The change in x is 3.
• If the rise is -6 and the run is 3, what is the gradient?


  The gradient is \( \frac{-6}{3} = -2 \).
• What are the methods to calculate the gradient from a graph?


  • Measure the rise for each unit across.
  • Use the rise over run equation.
  • Use the change in y over change in x equation.
• What are the characteristics of lines with different gradients?


  • Steep lines have higher gradients.
  • Flat lines have a gradient of zero.
  • Downward sloping lines have negative gradients.