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Lesson: Straight Line Equations in General Form

Sample Question Videos

Worksheet • 8 Questions • 1 Video

Q1:

Write the equation of the line that passes through the points ( 2 , βˆ’ 2 ) and ( βˆ’ 2 , 1 0 ) in the form π‘Ž π‘₯ + 𝑏 𝑦 + 𝑐 = 0 .

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

Q2:

Write the equation of the line with slope 3 2 and 𝑦 -intercept ( 0 , 3 ) in the form π‘Ž π‘₯ + 𝑏 𝑦 + 𝑐 = 0 .

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

Q3:

Does the equation 6 π‘₯ βˆ’ 2 𝑦 = 1 represent a straight line?

  • Ano
  • Byes

Q4:

A line passes through the points ( 4 , 3 ) and ( βˆ’ 2 , βˆ’ 9 ) .

Find the gradient of the line.

Find the coordinates of the point at which the line intercepts the 𝑦 -axis.

  • A ( 0 , βˆ’ 5 )
  • B ( βˆ’ 5 , 0 )
  • C ( 0 , 5 )
  • D ( 0 , 3 )
  • E ( 0 , βˆ’ 3 )

Hence, write the equation of the line in the form π‘Ž π‘₯ + 𝑏 𝑦 + 𝑐 = 0 .

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

Q5:

Which of the following equations represents a straight line?

  • A βˆ’ 7 π‘₯ βˆ’ 2 𝑦 = βˆ’ 9
  • B 𝑦 = √ π‘₯ + 6
  • C π‘₯ + √ 𝑦 = βˆ’ 5
  • D 𝑦 + 1 π‘₯ = βˆ’ 8

Q6:

Determine the general equation of a straight line that passes through point 𝑃 ( βˆ’ 6 , 6 ) and has a direction vector οƒ  𝐴 𝐡 , given that the coordinates of 𝐴 and 𝐡 are ( βˆ’ 2 , 3 ) and ( 2 , 0 ) , respectively.

  • A 3 π‘₯ + 4 𝑦 βˆ’ 6 = 0
  • B π‘₯ βˆ’ 2 = 0
  • C 3 π‘₯ βˆ’ 4 𝑦 + 6 = 0
  • D 4 π‘₯ + 3 𝑦 βˆ’ 6 = 0

Q7:

Determine the general equation of a straight line that passes through point 𝑃 ( βˆ’ 4 , βˆ’ 4 ) and has a direction vector οƒ  𝐴 𝐡 , given that the coordinates of 𝐴 and 𝐡 are ( 4 , 0 ) and ( 2 , βˆ’ 1 ) , respectively.

  • A π‘₯ βˆ’ 2 𝑦 βˆ’ 4 = 0
  • B π‘₯ + 6 𝑦 + 4 = 0
  • C π‘₯ + 2 𝑦 + 4 = 0
  • D 2 π‘₯ βˆ’ 𝑦 + 4 = 0

Q8:

Determine the general equation of a straight line that passes through point 𝑃 ( βˆ’ 6 , βˆ’ 3 ) and has a direction vector οƒ  𝐴 𝐡 , given that the coordinates of 𝐴 and 𝐡 are ( βˆ’ 4 , 5 ) and ( βˆ’ 5 , 1 ) , respectively.

  • A 4 π‘₯ βˆ’ 𝑦 + 2 1 = 0
  • B 4 π‘₯ βˆ’ 9 𝑦 + 2 9 = 0
  • C 4 π‘₯ + 𝑦 βˆ’ 2 1 = 0
  • D π‘₯ βˆ’ 4 𝑦 βˆ’ 2 1 = 0
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