Lesson Worksheet: Equation of a Straight Line: General Form Mathematics

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


Write the equation of the line that passes through the points (2,βˆ’2) and (βˆ’2,10) in the form π‘Žπ‘₯+𝑏𝑦+𝑐=0.

  • A4π‘₯+π‘¦βˆ’4=0
  • B4π‘₯+𝑦+4=0
  • C3π‘₯+𝑦+4=0
  • D3π‘₯βˆ’π‘¦βˆ’4=0
  • E3π‘₯+π‘¦βˆ’4=0


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

Hence, write the equation of the line in the form π‘Žπ‘₯+𝑏𝑦+𝑐=0.

  • A2π‘₯+𝑦+5=0
  • B2π‘₯βˆ’π‘¦βˆ’5=0
  • C2π‘₯βˆ’π‘¦βˆ’3=0
  • D2π‘₯βˆ’π‘¦+5=0
  • Eβˆ’2π‘₯βˆ’π‘¦βˆ’3=0


Write the equation of the line with slope 32 and 𝑦-intercept (0,3) in the form π‘Žπ‘₯+𝑏𝑦+𝑐=0.

  • A3π‘₯βˆ’2𝑦+3=0
  • B3π‘₯βˆ’2π‘¦βˆ’6=0
  • C3π‘₯βˆ’2𝑦+6=0
  • Dπ‘₯βˆ’2𝑦+6=0
  • E3π‘₯βˆ’π‘¦+6=0


What are the π‘₯-intercept and 𝑦-intercept of the line 3π‘₯+2π‘¦βˆ’12=0?

  • A2, 12
  • B3, 12
  • C4, 6
  • D2, 3
  • E3, 2


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

  • Aπ‘₯+𝑦+8=0
  • Bπ‘₯+π‘¦βˆ’8=0
  • Cπ‘₯βˆ’π‘¦+8=0
  • Dπ‘₯βˆ’π‘¦βˆ’8=0


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

  • A2π‘₯+𝑦+8=0
  • B2π‘₯+π‘¦βˆ’8=0
  • Cπ‘₯βˆ’2π‘¦βˆ’8=0
  • D2π‘₯βˆ’π‘¦+8=0


Given that the coordinates of the points 𝐴 and 𝐡 are (5,7) and (βˆ’4,4), respectively, and the point 𝐢 divides 𝐴𝐡 internally in the ratio 2∢1, determine the equation of the straight line passing through the points 𝐢 and 𝐷(βˆ’2,βˆ’2).

  • Aπ‘₯βˆ’7π‘¦βˆ’12=0
  • B7π‘₯βˆ’π‘¦+12=0
  • C7π‘₯+𝑦+12=0
  • D7π‘₯+π‘¦βˆ’12=0


Determine the area of the triangle bounded by the π‘₯-axis, the 𝑦-axis, and the straight line 2π‘₯+7𝑦+28=0.

  • A112 area units
  • B14 area units
  • C56 area units
  • D28 area units


Determine the equation of the straight line having a direction vector of u=⟨1,βˆ’2⟩, given that the line intersects the positive part of the 𝑦-axis at a point that is 6Β units away from the origin.

  • A2π‘₯βˆ’π‘¦βˆ’6=0
  • Bπ‘₯+2π‘¦βˆ’6=0
  • C2π‘₯βˆ’π‘¦+6=0
  • D2π‘₯+π‘¦βˆ’6=0


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‘Žπ‘₯+𝑏𝑦+𝑐=0.

  • Aβˆ’3π‘₯+π‘¦βˆ’3=0
  • Bβˆ’3π‘₯+4𝑦+3=0
  • C3π‘₯βˆ’4π‘¦βˆ’3=0
  • Dβˆ’3π‘₯+4π‘¦βˆ’3=0
  • Eβˆ’π‘₯+4π‘¦βˆ’3=0

This lesson includes 21 additional questions and 171 additional question variations for subscribers.

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