Chapter 10

• Gradient of a line

  The gradient is the rate of change of the y-coordinate with respect to the x-coordinate, usually represented as 'm'.
• Gradient-intercept form

  A straight line can be written in the form y = mx + c, where 'm' is the gradient and 'c' is the y-intercept.
• What is the general equation of a straight line?


  y = mx + c
• What does the variable 'm' represent in the equation of a straight line?


  'm' represents the gradient of the line
• What does the variable 'c' represent in the equation of a straight line?


  'c' represents the y-intercept of the line
• How is the gradient calculated in a straight line?


  The gradient is calculated as the change in y divided by the change in x
• What is the relationship between the gradients of parallel lines?


  Parallel lines have the same gradient
• What is the relationship between the gradients of perpendicular lines?


  The gradients of perpendicular lines multiply to make -1
• If the gradient of a line is -2, what is the gradient of a line perpendicular to it?


  The gradient of the perpendicular line is $-1/2$
• If the gradient of a line is 1/2, what is the gradient of a line perpendicular to it?

  The gradient of the perpendicular line is $-2$
• If the gradient of a line is 8, what is the gradient of a line perpendicular to it?


  The gradient of the perpendicular line is $-1/8$
• If the gradient of a line is -3/4, what is the gradient of a line perpendicular to it?


  The gradient of the perpendicular line is $4/3$
• If the gradient of a line is 1, what is the gradient of a line perpendicular to it?


  The gradient of the perpendicular line is $-1$
• What steps should be taken to find a line perpendicular to a given line?


  • Measure the y-intercept of the original line
  • Determine the gradient of the original line
  • Calculate the gradient of the perpendicular line (multiply original gradient by -1)
  • Use the y-intercept and new gradient to write the equation of the perpendicular line