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Lesson: Equation of a Line through Two Points

Video

14:60

Sample Question Videos

Worksheet • 21 Questions • 4 Videos

Q1:

A line 𝐿 passes through the points ( 3 , 3 ) and ( βˆ’ 1 , 0 ) . Work out the equation of the line, giving your answer in the form π‘Ž 𝑦 + 𝑏 π‘₯ + 𝑐 = 0 .

  • A 4 𝑦 βˆ’ 3 π‘₯ βˆ’ 3 = 0
  • B 4 𝑦 βˆ’ 3 π‘₯ + 3 = 0
  • C 𝑦 βˆ’ 3 π‘₯ βˆ’ 3 = 0
  • D βˆ’ 4 𝑦 + 3 π‘₯ βˆ’ 3 = 0
  • E 4 𝑦 βˆ’ π‘₯ βˆ’ 3 = 0

Q2:

A line 𝐿 passes through the points ( 2 , 3 ) and ( βˆ’ 2 , 5 ) . Work out the equation of the line, giving your answer in the form 𝑦 = π‘š π‘₯ + 𝑐 .

  • A 𝑦 = βˆ’ 1 2 π‘₯ + 4
  • B 𝑦 = 1 2 π‘₯ + 1 4
  • C 𝑦 = 1 2 π‘₯ + 2
  • D 𝑦 = 2 π‘₯ βˆ’ 1
  • E 𝑦 = βˆ’ 2 π‘₯ + 7

Q3:

A line 𝐿 passes through the points ( 1 , 1 ) and ( βˆ’ 5 , βˆ’ 1 ) . Work out the equation of the line, giving your answer in the form 𝑦 = π‘š π‘₯ + 𝑐 .

  • A 𝑦 = 1 3 π‘₯ + 2 3
  • B 𝑦 = 1 3 π‘₯ βˆ’ 2
  • C 𝑦 = π‘₯ βˆ’ 2
  • D 𝑦 = βˆ’ 3 π‘₯ + 4
  • E 𝑦 = 3 π‘₯ + 2

Q4:

Let 𝐴 be the point ( 5 , βˆ’ 1 ) and 𝐡 be the point ( βˆ’ 1 , 8 ) . Which of the following points is on βƒ–     βƒ— 𝐴 𝐡 ?

  • A ( 9 , βˆ’ 7 )
  • B ( 3 , βˆ’ 7 )
  • C ( βˆ’ 7 , 9 )
  • D ( βˆ’ 7 , 3 )
  • E ( 7 , 7 )

Q5:

What is the equation of the function seen in the given graph?

  • A 𝑦 = π‘₯ βˆ’ 1
  • B 𝑦 = π‘₯ βˆ’ 4
  • C 𝑦 = π‘₯ + 1
  • D 𝑦 = π‘₯ + 4
  • E π‘₯ = 𝑦 βˆ’ 1

Q6:

The following graph shows the money that Farida earns.

Write an equation to represent the relationship between dollars and time.

  • A
  • B
  • C
  • D
  • E

Q7:

Find the equation that represents the relation between π‘₯ and 𝑦 .

  • A 𝑦 = π‘₯ βˆ’ 3
  • B 𝑦 = 3 π‘₯
  • C 𝑦 = π‘₯ + 3
  • D 𝑦 = π‘₯ 3
  • E 𝑦 = 3 π‘₯

Q8:

The line through points ( 3 , βˆ’ 3 ) and ( 8 , 1 ) has equation 𝑦 = π‘Ž π‘₯ βˆ’ 4 . What is π‘Ž ?

  • A 4 5
  • B 5 4
  • C βˆ’ 5 4
  • D βˆ’ 4 5

Q9:

Suppose that 𝐴 𝐡 is a chord of a circle 𝑀 , 𝐷 is the midpoint of 𝐴 𝐡 , and the coordinates of 𝐴 and 𝐡 are ( 1 , 4 ) and ( 3 , 5 ) . Find the equation of βƒ–       βƒ— 𝑀 𝐷 .

  • A 𝑦 = βˆ’ 2 π‘₯ + 1 7 2
  • B 𝑦 = 1 2 π‘₯ + 1 7 2
  • C 𝑦 = 1 2 π‘₯ + 2
  • D 𝑦 = βˆ’ 2 π‘₯ + 2

Q10:

Determine the equation of the straight line given in the diagram.

  • A π‘₯ βˆ’ 2 𝑦 = 0
  • B π‘₯ + 2 𝑦 = 0
  • C 𝑦 + 2 π‘₯ = 0
  • D 𝑦 βˆ’ 2 π‘₯ = 0

Q11:

A line 𝐿 passes through the points ( βˆ’ 2 , 4 ) and ( 4 , βˆ’ 3 ) . Work out the equation of the line, giving your answer in the form 𝑦 = π‘š π‘₯ + 𝑐 .

  • A 𝑦 = βˆ’ 7 6 π‘₯ + 5 3
  • B 𝑦 = βˆ’ 7 6 π‘₯ + 3 5
  • C 𝑦 = βˆ’ 7 6 π‘₯ + 1 9 3
  • D 𝑦 = βˆ’ 6 7 π‘₯ + 1 6 7
  • E 𝑦 = βˆ’ 6 7 π‘₯ + 4 0 7

Q12:

A line 𝐿 passes through the points ( βˆ’ 1 , 2 ) and ( 3 , 6 ) . Work out the equation of the line, giving your answer in the form 𝑦 = π‘š π‘₯ + 𝑐 .

  • A 𝑦 = π‘₯ + 3
  • B 𝑦 = βˆ’ π‘₯ + 2
  • C 𝑦 = βˆ’ π‘₯ βˆ’ 3
  • D 𝑦 = βˆ’ π‘₯
  • E 𝑦 = βˆ’ π‘₯ βˆ’ 1

Q13:

Given that the points ( βˆ’ 1 , βˆ’ 4 ) , ( 3 , 𝑦 ) , and ( βˆ’ 5 , βˆ’ 6 ) are collinear, find the value of 𝑦 .

Q14:

Find the equation of the straight line which passes through the two points ( βˆ’ 1 , βˆ’ 2 ) and ( βˆ’ 7 , βˆ’ 4 ) .

  • A 𝑦 = 1 3 π‘₯ βˆ’ 5 3
  • B 𝑦 = 3 π‘₯ + 1
  • C 𝑦 = 1 3 π‘₯ βˆ’ 1 3
  • D 𝑦 = 3 4 π‘₯ βˆ’ 5 4

Q15:

Find the equation of the straight line which passes through the two points ( 1 , 4 ) and ( 5 , 6 ) .

  • A 𝑦 = 1 2 π‘₯ + 7 2
  • B 𝑦 = 2 π‘₯ + 2
  • C 𝑦 = 1 2 π‘₯ βˆ’ 1
  • D 𝑦 = 5 3 π‘₯ + 7 3

Q16:

Find the equation of the straight line which passes through the two points ( βˆ’ 1 , 2 ) and ( 3 , βˆ’ 4 ) .

  • A 𝑦 = βˆ’ π‘₯ + 1 2
  • B 𝑦 = βˆ’ 2 3 π‘₯ + 4 3
  • C 𝑦 = βˆ’ 3 2 π‘₯ + 2
  • D 𝑦 = βˆ’ π‘₯ + 1

Q17:

Find the equation of the straight line which passes through the two points ( βˆ’ 2 , βˆ’ 3 ) and ( 4 , 7 ) .

  • A 𝑦 = 5 3 π‘₯ + 1 3
  • B 𝑦 = 3 5 π‘₯ βˆ’ 9 5
  • C 𝑦 = 5 3 π‘₯ + 3
  • D 𝑦 = 2 π‘₯ + 1

Q18:

If 𝐴 𝐡 𝐢 𝐷 is a square in which 𝐴 ( 8 , 1 ) and 𝐢 ( βˆ’ 3 , 5 ) , find the equation of βƒ–     βƒ— 𝐡 𝐷 in the form of 𝑦 = π‘š π‘₯ + 𝑐 .

  • A 𝑦 = 1 1 4 π‘₯ βˆ’ 3 1 8
  • B 𝑦 = βˆ’ 4 1 1 π‘₯ + 4 3 1 1
  • C 𝑦 = 4 1 1 π‘₯ + 2 3 1 1
  • D 𝑦 = βˆ’ 1 1 4 π‘₯ + 7 9 8

Q19:

In the figure shown, points 𝐴 and 𝐡 have coordinates ( 8 , 0 ) and ο€Ό 0 , βˆ’ 5 2  . Determine 𝐢 and then the equation of the line βƒ–     βƒ— 𝐴 𝐢 .

  • A ( βˆ’ 8 , βˆ’ 5 ) , 𝑦 = 5 1 6 π‘₯ βˆ’ 5 2
  • B ο€Ό βˆ’ 8 , βˆ’ 5 2  , 𝑦 = 1 6 5 π‘₯ βˆ’ 5 2
  • C ( βˆ’ 8 , βˆ’ 5 ) , 𝑦 = βˆ’ 5 1 6 π‘₯ βˆ’ 5 2
  • D ο€Ό 4 , βˆ’ 5 4  , 𝑦 = 5 1 6 π‘₯ βˆ’ 5 2

Q20:

Determine, in the form 𝑦 = π‘š π‘₯ + 𝑐 , the equation of the axis of symmetry of 𝐴 𝐡 , where the coordinates of 𝐴 and 𝐡 are ( βˆ’ 3 , 4 ) and ( 1 , 5 ) respectively.

  • A 𝑦 = βˆ’ 4 π‘₯ + 1 2
  • B 𝑦 = 1 4 π‘₯ + 1 9 4
  • C 𝑦 = 1 2 π‘₯ βˆ’ 4
  • D 𝑦 = βˆ’ 4 π‘₯ + 1

Q21:

Find the linear equation that includes the two points (2, 3) and (0, 6).

  • A 𝑦 = βˆ’ 1 . 5 π‘₯ + 6
  • B 𝑦 = βˆ’ 6 π‘₯ + 1 . 5
  • C 𝑦 = 2 π‘₯ + 3
  • D 𝑦 = 0 . 6 6 π‘₯ + 6
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