Worksheet: Slope of a Line through Two Points

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In this worksheet, we will practice finding the slope of a line that goes through two given points.

Q1:

Line 1 passes through point 𝐴(βˆ’6,17) and point 𝐡(βˆ’18,βˆ’14) and Line 2 passes through the points 𝐢(βˆ’12,18) and 𝐷(βˆ’9,20). Which of the two lines has a steeper slope?

  • Aline 1
  • Bline 2

Q2:

Determine the slope of the line that passes through the points 𝐴(2,βˆ’5) and 𝐡(4,5).

  • A βˆ’ 5
  • B5
  • C βˆ’ 1 7
  • D βˆ’ 1 5
  • E 1 5

Q3:

What is the value of 𝑦 so that 𝐴(βˆ’9,6), 𝐡(3,βˆ’3), and 𝐢(βˆ’1,𝑦) are collinear?

Q4:

In this figure, the slope of ⃖⃗𝐴𝐡 is .

  • Anegative
  • Bpositive
  • Cundefined
  • Dzero

Q5:

Given that the slope of the line passing through (βˆ’2,7), (π‘₯,3), and (5,𝑦) is βˆ’1, find the values of π‘₯ and 𝑦.

  • A π‘₯ = 2 , 𝑦 = 0
  • B π‘₯ = βˆ’ 2 , 𝑦 = 3
  • C π‘₯ = 4 , 𝑦 = βˆ’ 7
  • D π‘₯ = βˆ’ 2 , 𝑦 = 0
  • E π‘₯ = 2 , 𝑦 = βˆ’ 3

Q6:

𝐿 𝑀 𝑁 is a right-angled triangle at 𝐿 where π‘šβˆ π‘€=45∘ and the coordinates of 𝐿 and 𝑀 are 𝐿(0,βˆ’8) and 𝑀(3,βˆ’8) respectively. Find the coordinates of 𝑁 given the slope of 𝑀𝑁 is βˆ’1.

  • A ( 0 , βˆ’ 1 1 )
  • B ( 3 , βˆ’ 8 )
  • C ( 3 , βˆ’ 5 )
  • D ( βˆ’ 3 , βˆ’ 8 )
  • E ( 0 , βˆ’ 5 )

Q7:

What is the slope of a line passing through the points (3,5) and (7,9)?

Q8:

True or False: Given a non vertical line, the slopes between any two of its points will be equal.

  • Atrue
  • Bfalse

Q9:

Which of the following characteristics does the line that passes through the points (βˆ’7,βˆ’6.75), (3,βˆ’14.25), and (βˆ’2,βˆ’10.5) have?

  • Aa positive slope and a positive 𝑦-intercept
  • Ba negative slope and a positive 𝑦-intercept
  • Ca positive slope and a negative 𝑦-intercept
  • Da negative slope and a negative 𝑦-intercept

Q10:

Given that the slope of a straight line passing through the points (9,βˆ’7) and (βˆ’3,π‘˜) is βˆ’512, find the value of π‘˜.

Q11:

βƒ–     βƒ— 𝐴 𝐡 is parallel to the 𝑦-axis. If the coordinates of the points 𝐴 and 𝐡 are (π‘š,2) and (8,6), respectively, find the value of π‘š.

Q12:

Find the value of 𝑦 such that the straight line passing through (3,βˆ’12) and (βˆ’5,3𝑦) is perpendicular to the 𝑦-axis.

Q13:

Given that the straight line passing through the points (1,8) and (βˆ’6,π‘˜) is parallel to the π‘₯-axis, find the value of π‘˜.

Q14:

βƒ–     βƒ— 𝐴 𝐡 is parallel to the π‘₯-axis. If the coordinates of the point 𝐴 and 𝐡 are (7,βˆ’2) and (βˆ’7,π‘˜), respectively, find the value of π‘˜.

Q15:

In this figure, the slope of ⃖⃗𝐡𝐢 is .

  • Azero
  • Bundefined
  • Cpositive
  • Dnegative

Q16:

In this figure, the slope of ⃖⃗𝐴𝑂 is .

  • Anegative
  • Bpositive
  • Cundefined
  • Dzero

Q17:

In this figure, the slope of ⃖⃗𝐴𝐢 is .

  • Anegative
  • Bzero
  • Cpositive
  • Dundefined

Q18:

What is the slope of the line passing through the points ο€Ό2,23 and (6,2)?

  • A4
  • B3
  • C βˆ’ 3
  • D 1 3
  • E βˆ’ 1 3

Q19:

If a line has a positive slope, what can be said of the angle it makes with the positive π‘₯-axis?

  • AIt is a right angle.
  • BIt is a zero angle.
  • CIt is an obtuse angle.
  • DIt is an acute angle.

Q20:

What can be said of the slope of a line that is parallel to the 𝑦-axis?

  • AIt is 1.
  • BIt is undefined.
  • CIt is 0.
  • DIt is βˆ’1.

Q21:

Consider the two points 𝐴(π‘₯,𝑦) and 𝐡(π‘₯,𝑦).

Find an expression for the slope of the line on 𝐴 and 𝐡.

  • A π‘₯ βˆ’ π‘₯ 𝑦 βˆ’ 𝑦    
  • B 𝑦 βˆ’ 𝑦 π‘₯ βˆ’ π‘₯    
  • C 𝑦 + 𝑦 π‘₯ + π‘₯    
  • D 𝑦 βˆ’ 𝑦 π‘₯ βˆ’ π‘₯    
  • E π‘₯ + π‘₯ 𝑦 + 𝑦    

Find the slope of the line segment connecting the points (3,4) and (5,7). Give your answer as a fraction in its simplest form.

  • A 1 1 8
  • B 2 3
  • C 1 1 2
  • D 3 2
  • E 8 1 1

Q22:

What is the slope of the line passing through the points (2,βˆ’2) and (4,8)?

Q23:

What is the slope of the line passing through (2,14) and (3,22)?

Q24:

Find the slope of the straight line which passes through the points (βˆ’9,4) and (βˆ’6,βˆ’2).

  • A βˆ’ 2 1 5
  • B2
  • C 1 2
  • D βˆ’ 1 2
  • E βˆ’ 2

Q25:

Given that the points 𝐴(12,10) and 𝐡(π‘₯,βˆ’8) lie on a line that has a slope of 1, determine the value of π‘₯.

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