straight line

• gradient


  • represented by$M$
  • measure of steepness of slope
  • positive gradient - the line is increasing
  • negative gradient - the line is decreasing
• y-intercept 


  • represented by $c$
  • shows where the line cuts the y-axis
  • find by making x = 0
• find the gradient of a line joining two points

  step 1: select two coordinates

  step 2: label them (x1, y1) (x2, y2)

  step 3: substitute them into gradient formula
• find the gradient of a line joining two points example


  (-4,4), (12,-28)

  m =$\frac{y_2-\ y_1}{x_2-x_1}$ = $\frac{\left(-28\right)-\ 4}{12-\left(-4\right)}$ = $\frac{-32}{16}$ = $-2$
• find equation of a line (from gradient and y-intercept)


  step 1: find gradient m

  step 2: find y-intercept c

  step 3: substitute into y = mx + c
• find equation of a line (from two points)


  • use this when there are only two points (ex. no y-intercept)

  step 1: find gradient

  Step 2: substitute into y – b = m(x – a), where (a, b) are taken from either one of the points