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Lesson Worksheet: Equation of a Straight Line: General Form Mathematics • 9th Grade

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

Q1:

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

Q2:

A straight line has the equation βˆ’15π‘₯+3π‘¦βˆ’12=0. What is the slope of the line?

Q3:

If the slope of the straight line (3π‘Ž+7)π‘₯+4π‘Žπ‘¦+4=0 equals βˆ’1, find the value of π‘Ž.

Q4:

Determine the equation of the line which cuts the π‘₯-axis at 4 and the 𝑦-axis at 7.

  • A7π‘₯+4𝑦+28=0
  • Bβˆ’4π‘₯+7π‘¦βˆ’28=0
  • C4π‘₯+7π‘¦βˆ’28=0
  • D7π‘₯+4π‘¦βˆ’28=0

Q5:

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

Q6:

Find the equation of the line that passes through the points 𝐴(βˆ’10,2) and 𝐡(0,5), giving your answer in the form π‘Žπ‘₯+𝑏𝑦+𝑐=0.

  • A3π‘₯+10π‘¦βˆ’50=0
  • B10π‘₯+3π‘¦βˆ’50=0
  • C10π‘₯+3π‘¦βˆ’15=0
  • Dβˆ’10π‘₯+3π‘¦βˆ’15=0
  • Eβˆ’3π‘₯+10π‘¦βˆ’50=0

Q7:

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

Q8:

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

Q9:

Given 𝐴(βˆ’3,βˆ’2), 𝐡(0,5), and 𝐢(2,βˆ’6), find the equation of the straight line that passes through the vertex 𝐴 and bisects 𝐡𝐢.

  • A3π‘₯+π‘¦βˆ’7=0
  • B3π‘₯+8π‘¦βˆ’7=0
  • Cβˆ’3π‘₯+𝑦+7=0
  • Dβˆ’3π‘₯+8𝑦+7=0

Q10:

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

This lesson includes 37 additional questions and 180 additional question variations for subscribers.

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