Chapter 5 - Straight Line Graphs

• How can you define a straight line?


  By giving one point on the line and the gradient or two different points on the line
• What is the equation of a line with gradient m that passes through the point (x₁, y₁)?


  y - y₁ = m(x - x₁)
• What do parallel lines have in common?


  They have the same gradient
• What characterizes perpendicular lines?


  They are at right angles to each other
• What is the product of the gradients of two perpendicular lines?


  • 1
• How can you find the point of intersection of two lines?


  By using simultaneous equations
• What does it mean for two quantities to be in direct proportion?


  They increase at the same rate
• What does the graph of two quantities in direct proportion look like?


  It is a straight line through the origin
• What is the general form of the equation of a straight line?


  y = mx + c
• What is another form of the equation of a straight line?

  ax + by + c = 0
• What is a mathematical model?


  An attempt to represent a real-life situation using mathematical concepts
• Why is it often necessary to make assumptions when creating a mathematical model?


  To simplify real-life problems for easier representation
• What is the formula to calculate the gradient of a straight line joining two points?



  $m =$$\frac{y_2 - y_1}{x_2 - x_1}$
• If a line has a gradient of m, what is the gradient of a line perpendicular to it?


  it is $\frac{1}{m}$
• What is the formula for the gradient of a straight line?


  $m =$$\frac{y_2 - y_1}{x_2 - x_1}$
• What are the two equation forms of a straight line?


  y = mx + c and ax + by + c = 0
• How do you write the equation of a line through a specific point?


  y - y₁ = m(x - x₁)
• What is true about the gradients of parallel lines?


  Parallel lines have the same gradient.
• What is the gradient of a line that is perpendicular to another line with gradient m?


  $-\frac{1}{m}$
• What is the product of the gradients of two perpendicular lines?

  • -1
• How can the intersection of two lines be found?


  Using simultaneous equations.
• What does direct proportion mean in relation to quantities?


  Quantities that increase at the same rate.
• What do mathematical models represent?


  Real-life situations with assumptions.
• How can you find the distance d between two points (x₁, y₁) and (x₂, y₂)?



  using the formula: d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}