Worksheet: Equation of a Straight Line from the Slope and y-Intercept

In this worksheet, we will practice finding the equation of a straight line in different forms given its slope and its y-intercept.

Q1:

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

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

Q2:

Which equation represents the line shown?

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

Q3:

Find the equation of the straight line represented by the graph below in the form of 𝑦 = π‘š π‘₯ + 𝑐 .

  • A 𝑦 = 8 π‘₯ βˆ’ 9
  • B 𝑦 = βˆ’ 8 π‘₯ βˆ’ 9
  • C 𝑦 = βˆ’ 2 π‘₯ + 3
  • D 𝑦 = βˆ’ 8 3 π‘₯ + 5 3
  • E 𝑦 = 2 π‘₯ βˆ’ 3

Q4:

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’ 3 7 π‘₯ + 7 , area of triangle = 21 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’ 7 3 π‘₯ + 7 , area of triangle = 10.5 square units

Q5:

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

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

Q6:

Determine, in slope-intercept form, the equation of the line which has a slope of 8 and a 𝑦 -intercept of βˆ’ 4 .

  • A 𝑦 = βˆ’ 4 π‘₯ + 8
  • B 𝑦 = 8 π‘₯ + 4
  • C 𝑦 = βˆ’ 4 π‘₯ βˆ’ 8
  • D 𝑦 = 8 π‘₯ βˆ’ 4
  • E 𝑦 = π‘₯ βˆ’ 4

Q7:

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

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

Q8:

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

  • A
  • B
  • C
  • D
  • E

Q9:

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

  • A
  • B
  • C
  • D
  • E

Q10:

In the figure below, 𝐴 is the point ( 0 , βˆ’ 4 ) and t a n ∠ 𝐴 𝐡 𝑂 = 4 7 . Find the coordinates of 𝐡 , the slope of βƒ–     βƒ— 𝐴 𝐡 , and the equation of the perpendicular to βƒ–     βƒ— 𝐴 𝐡 that passes through 𝑂 in the form 𝑦 = π‘š π‘₯ + 𝑐 .

  • A ( βˆ’ 4 , 0 ) , βˆ’ 7 4 , 𝑦 = 4 7 π‘₯
  • B ( βˆ’ 7 , 0 ) , 4 7 , 𝑦 = 4 7 π‘₯
  • C ( βˆ’ 7 , 0 ) , βˆ’ 4 7 , 𝑦 = βˆ’ 4 7 π‘₯ βˆ’ 4
  • D ( βˆ’ 7 , 0 ) , βˆ’ 4 7 , 𝑦 = 7 4 π‘₯
  • E ( 4 , 0 ) , βˆ’ 7 , 𝑦 = 1 7 π‘₯ βˆ’ 4

Q11:

Find the coordinates of the 𝑦 -intercept and the slope of the straight line whose equation is βˆ’ 5 4 π‘₯ + 2 𝑦 = 9 .

  • A ( 0 , 9 ) , 5 4
  • B ( 0 , 9 ) , 2 5
  • C ο€Ό 0 , 9 2  , βˆ’ 5 8
  • D ο€Ό 0 , 9 2  , 5 8
  • E ο€Ό 0 , βˆ’ 3 6 5  , 8 5

Q12:

Find the equation, in the form 𝑦 = π‘š π‘₯ + 𝑐 , of the line with slope βˆ’ 8 3 and 𝑦 -intercept 1 0 .

  • A 𝑦 = βˆ’ 3 8 π‘₯ + 1 0
  • B 𝑦 = 1 0 π‘₯ βˆ’ 8 3
  • C 𝑦 = 8 3 π‘₯ + 1 0
  • D 𝑦 = βˆ’ 8 3 π‘₯ + 1 0

Q13:

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

  • Ano
  • Byes

Q14:

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

  • Ano
  • Byes

Q15:

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

  • Ayes
  • Bno

Q16:

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

Q17:

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

Q18:

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.

Q19:

A straight line has the equation 3 𝑦 βˆ’ 1 5 π‘₯ βˆ’ 1 2 = 0 . What is the slope of the line?

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