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Lesson: Finding the Equation of a Straight Line in Different Forms given the Slope and y-Intercept

Video

11:42

Sample Question Videos

Worksheet • 19 Questions • 2 Videos

Q1:

Write the equation represented by the graph shown. Give your answer in the form π‘₯ + 𝑦 = 𝑐 .

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

Q2:

Which equation represents the line shown?

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

Q3:

In the figure below, is the point and . Find the coordinates of , the gradient of , and the equation of the perpendicular to that passes through in the form .

  • A , ,
  • B , ,
  • C , ,
  • D , ,
  • E , ,

Q4:

Write the equation represented by the graph shown. Give your answer in the form 𝑦 = π‘š π‘₯ + 𝑏 .

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

Q5:

The graph of the equation 𝑦 + 2 = 5 ( π‘₯ + 1 ) is a straight line.

What is the slope of the line?

Which one of the following points lies on the line?

  • A ( βˆ’ 1 , βˆ’ 2 )
  • B ( βˆ’ 2 , 5 )
  • C ( 1 , 5 )
  • D ( 5 , βˆ’ 2 )
  • E ( βˆ’ 2 , βˆ’ 1 )

Q6:

Find the coordinates of the point where 𝑦 = 4 π‘₯ + 1 2 intersects the 𝑦 -axis.

  • A ( 0 , 1 2 )
  • B ( 0 , βˆ’ 3 )
  • C ( 4 , βˆ’ 3 )
  • D ( 4 , 0 )

Q7:

Find the coordinates of the point where 𝑦 = 3 π‘₯ + 9 intersects the 𝑦 -axis.

  • A ( 0 , 9 )
  • B ( 0 , βˆ’ 3 )
  • C ( 3 , βˆ’ 3 )
  • D ( 3 , 0 )

Q8:

Which of the following graphs represents the equation 𝑦 = βˆ’ 5 π‘₯ βˆ’ 2 ?

  • A
  • B
  • C
  • D
  • E

Q9:

Does the point ( 4 , βˆ’ 1 1 ) lie on the line 𝑦 = βˆ’ 2 π‘₯ βˆ’ 4 ?

  • Ayes
  • Bno

Q10:

The line π‘₯ βˆ’ 2 βˆ’ 5 = 𝑦 βˆ’ 2 βˆ’ 7 = 𝑧 βˆ’ 1 βˆ’ 1 0 passes through the sphere π‘₯ + 𝑦 + 𝑧 βˆ’ 1 8 π‘₯ + 8 𝑦 + 1 4 𝑧 + 2 8 = 0 2 2 2 . Find the length of the line segment between the two points of intersection of the line and the sphere. Give your answer to the nearest hundredth.

Q11:

Find the equation of the line with π‘₯ -intercept 3 and 𝑦 -intercept 7, and calculate the area of the triangle on this line and the two coordinate axes.

  • A 𝑦 = βˆ’ 7 3 π‘₯ + 7 , area of triangle = 10.5 square units
  • B 𝑦 = 3 1 0 π‘₯ βˆ’ 7 , area of triangle = 10.5 square units
  • C 𝑦 = βˆ’ 7 3 π‘₯ + 7 , area of triangle = 21 square units
  • D 𝑦 = βˆ’ 3 7 π‘₯ + 7 , area of triangle = 21 square units

Q12:

Find the equation of the line with π‘₯ -intercept 4 and 𝑦 -intercept 9, and calculate the area of the triangle on this line and the two coordinate axes.

  • A 𝑦 = βˆ’ 9 4 π‘₯ + 9 , area of triangle = 18 square units
  • B 𝑦 = 4 1 3 π‘₯ βˆ’ 9 , area of triangle = 18 square units
  • C 𝑦 = βˆ’ 9 4 π‘₯ + 9 , area of triangle = 36 square units
  • D 𝑦 = βˆ’ 4 9 π‘₯ + 9 , area of triangle = 36 square units

Q13:

Find the equation of the line with π‘₯ -intercept 3 and 𝑦 -intercept 5, and calculate the area of the triangle on this line and the two coordinate axes.

  • A 𝑦 = βˆ’ 5 3 π‘₯ + 5 , area of triangle = 7.5 square units
  • B 𝑦 = 3 8 π‘₯ βˆ’ 5 , area of triangle = 7.5 square units
  • C 𝑦 = βˆ’ 5 3 π‘₯ + 5 , area of triangle = 15 square units
  • D 𝑦 = βˆ’ 3 5 π‘₯ + 5 , area of triangle = 15 square units

Q14:

Find the coordinates of the -intercept and the gradient of the straight line whose equation is .

  • A ,
  • B ,
  • C ,
  • D ,
  • E ,

Q15:

Does the point ( 2 , βˆ’ 3 ) lie on the line 𝑦 = 5 π‘₯ βˆ’ 7 ?

  • Ayes
  • Bno

Q16:

Does the point ο€Ό 1 , βˆ’ 9 2  lie on the line 𝑦 = 1 2 π‘₯ βˆ’ 5 ?

  • Ano
  • Byes

Q17:

Find the equation, in the form , of the line with gradient and -intercept .

  • A
  • B
  • C
  • D

Q18:

Which of the following graphs represents the equation 𝑦 = 2 π‘₯ 3 βˆ’ 2 ?

  • A
  • B
  • C
  • D
  • E

Q19:

What is the slope of the line that passes through the point ( 4 , 1 8 ) and intercepts 𝑦 at βˆ’ 2 ?

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