GRAPH

• 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?


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


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


  By finding the rise and run between the two points and using the equation rise/run.
• What is the gradient of a line that does not rise at all?


  The gradient is zero.
• 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 negative 2.
• How can you find the gradient using two points on a line?


  By calculating the rise from one point to the other and dividing it by the run between those points.
• If the y-values change from 3 to -3 and the x-values change from -1 to 2, what is the gradient?


  The gradient is negative 2.
• What are the three methods to calculate the gradient from a graph?


  • Measure how much the line rises for each unit it goes 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.
• How do you find the gradient for longer stretches of a graph?


  1. Identify two points on the line.
  2. Calculate the rise (change in y).
  3. Calculate the run (change in x).
  4. Use the equation: gradient = rise/run.