Worksheet: Straight Line Equations in General Form

In this worksheet, we will practice finding and writing the equation of a straight line in general form.

Q1:

Write the equation of the line that passes through the points ( 2 , 2 ) and ( 2 , 1 0 ) in the form 𝑎 𝑥 + 𝑏 𝑦 + 𝑐 = 0 .

  • A 3 𝑥 + 𝑦 + 4 = 0
  • B 3 𝑥 + 𝑦 4 = 0
  • C 3 𝑥 𝑦 4 = 0
  • D 4 𝑥 + 𝑦 4 = 0
  • E 4 𝑥 + 𝑦 + 4 = 0

Q2:

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

  • A 𝑥 2 = 0
  • B 4 𝑥 + 3 𝑦 6 = 0
  • C 3 𝑥 4 𝑦 + 6 = 0
  • D 3 𝑥 + 4 𝑦 6 = 0

Q3:

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

Find the gradient of the line.

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

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

Hence, write the equation of the line in the form 𝑎 𝑥 + 𝑏 𝑦 + 𝑐 = 0 .

  • A 2 𝑥 𝑦 3 = 0
  • B 2 𝑥 𝑦 3 = 0
  • C 2 𝑥 𝑦 + 5 = 0
  • D 2 𝑥 𝑦 5 = 0
  • E 2 𝑥 + 𝑦 + 5 = 0

Q4:

Write the equation of the line with slope 3 2 and 𝑦 -intercept ( 0 , 3 ) in the form 𝑎 𝑥 + 𝑏 𝑦 + 𝑐 = 0 .

  • A 3 𝑥 𝑦 + 6 = 0
  • B 3 𝑥 2 𝑦 + 3 = 0
  • C 3 𝑥 2 𝑦 6 = 0
  • D 3 𝑥 2 𝑦 + 6 = 0
  • E 𝑥 2 𝑦 + 6 = 0

Q5:

Which of the following equations represents a straight line?

  • A 𝑥 + 𝑦 = 5
  • B 7 𝑥 2 𝑦 = 9
  • C 𝑦 = 𝑥 + 6
  • D 𝑦 + 1 𝑥 = 8

Q6:

Does the equation 6 𝑥 2 𝑦 = 1 represent a straight line?

  • Ayes
  • Bno

Q7:

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

  • A 𝑥 + 2 𝑦 + 4 = 0
  • B 𝑥 2 𝑦 4 = 0
  • C 𝑥 + 6 𝑦 + 4 = 0
  • D 2 𝑥 𝑦 + 4 = 0

Q8:

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

  • A 4 𝑥 + 𝑦 2 1 = 0
  • B 4 𝑥 9 𝑦 + 2 9 = 0
  • C 4 𝑥 𝑦 + 2 1 = 0
  • D 𝑥 4 𝑦 2 1 = 0

Q9:

Given that the line 2 𝑥 8 𝑦 = 𝑎 intersects the 𝑥 -axis at the point ( 4 , 𝑏 ) , find the values of 𝑎 and 𝑏 .

  • A 𝑎 = 0 , 𝑏 = 8
  • B 𝑎 = 8 , 𝑏 = 0
  • C 𝑎 = 4 , 𝑏 = 8
  • D 𝑎 = 3 2 , 𝑏 = 0

Q10:

What are the 𝑥 - and 𝑦 - intercepts of the line 3 𝑥 + 2 𝑦 1 2 = 0 ?

  • A3, 12
  • B3, 2
  • C2, 3
  • D2, 12

Q11:

A line passes through ( 5 , 3 ) and cuts out a triangle of area 32 with the two coordinate axes. What is its equation?

  • A 𝑥 𝑦 + 8 = 0
  • B 𝑥 + 𝑦 8 = 0
  • C 𝑥 𝑦 8 = 0
  • D 𝑥 + 𝑦 + 8 = 0

Q12:

Find all the lines that pass through ( 3 , 2 ) and whose 𝑥 - and 𝑦 -intercepts combined distances from the origin is 12.

  • A 𝑥 2 𝑦 8 = 0
  • B 2 𝑥 + 𝑦 8 = 0
  • C 2 𝑥 + 𝑦 + 8 = 0
  • D 2 𝑥 𝑦 + 8 = 0

Q13:

Given that the coordinates of the points 𝐴 and 𝐵 are ( 5 , 7 ) and ( 4 , 4 ) , respectively, and the point 𝐶 divides 𝐴 𝐵 internally in the ratio 2 1 , determine the equation of the straight line passing through the points 𝐶 and 𝐷 ( 2 , 2 ) .

  • A 7 𝑥 𝑦 + 1 2 = 0
  • B 𝑥 7 𝑦 1 2 = 0
  • C 7 𝑥 + 𝑦 + 1 2 = 0
  • D 7 𝑥 + 𝑦 1 2 = 0

Q14:

Determine the area of the triangle bounded by the 𝑥 - a x i s , the 𝑦 - a x i s , and the straight line 2 𝑥 + 7 𝑦 + 2 8 = 0 .

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