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Topics · Straight Lines

Equations of straight lines in DSE Maths Paper 2

Straight lines are the first step of coordinate geometry. You need to find the equation of a line from a point and a slope, or from two points, read the slope and intercepts off an equation, and use the conditions for two lines to be parallel or perpendicular.

What this topic covers

  • Slope, x-intercept and y-intercept
  • Point-slope and two-point forms; the general form Ax + By + C = 0
  • Parallel and perpendicular lines
  • Mid-points and lines through them

Read the study guide on this topic

Two sample questions

Sample 1

The equation of the straight line L sub 1 is 5x plus 3y minus 3 equals 0. If the straight line L sub 2 passes through ( negative 3, negative 1) and is perpendicular to L sub 1, then the equation of L sub 2 is

  1. A3x minus 5y plus 4 equals 0.
  2. B5x minus 3y plus 12 equals 0.
  3. C3x minus 5y minus 4 equals 0.
  4. D3x plus 5y plus 14 equals 0.
Show the answer and solution

Answer: A

Worked solution

Slope of L1=−53⇒\displaystyle L_1 = -\frac{5}{3} \Rightarrowslope of L2=35\displaystyle L_2 = \frac{3}{5}L2:y\displaystyle L_2: y−(−1)\displaystyle {}- (-1)=35(x−(−3))\displaystyle {}= \frac{3}{5}\left(x - (-3)\right)⇒3x−5y+4=0\displaystyle \Rightarrow 3x - 5y + 4 = 0

Sample 2

The coordinates of the points A, B and C are (2, 0), ( negative 4, negative 8) and (5, negative 6) respectively. Find the equation of the straight line which passes through C and the mid-point of AB.

  1. A3x plus 4y plus 19 equals 0
  2. B3x minus y minus 21 equals 0
  3. Cx plus 3y plus 13 equals 0
  4. D3x plus y minus 9 equals 0
Show the answer and solution

Answer: C

Worked solution

Mid-point of AB=M(−1,−4)\displaystyle AB = M(-1, -4)Slope of CM=−4−(−6)−1−5=−13\displaystyle CM = \dfrac{-4 - (-6)}{-1 - 5} = -\frac{1}{3}y\displaystyle y−(−6)\displaystyle {}- (-6)=−13(x−5)\displaystyle {}= -\frac{1}{3}\left(x - 5\right)⇒x\displaystyle {}\Rightarrow x+3y\displaystyle {}+ 3y+13\displaystyle {}+ 13=0\displaystyle {}= 0

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Original material by Dsetopia, written from the EDB syllabus learning objectives. Not affiliated with the HKEAA; no exam content is reproduced.