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Lesson: Slope from Two Points

In this lesson, we will learn how to calculate the slope of a line given two points that lie on it and find the coordinates of a point on a line where another point and the slope are known.

Video

06:02

Sample Question Videos

02:49
01:19
02:22

Worksheet • 23 Questions • 5 Videos

Q1:

Line 1 passes through point 𝐴 ( βˆ’ 6 , 1 7 ) and point 𝐡 ( βˆ’ 1 8 , βˆ’ 1 4 ) and Line 2 passes through the points 𝐢 ( βˆ’ 1 2 , 1 8 ) and 𝐷 ( βˆ’ 9 , 2 0 ) . Which of the two lines has a steeper slope?

  • Aline 2
  • Bline 1

Q2:

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

  • A5
  • B βˆ’ 1 7
  • C βˆ’ 5
  • 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:

Given that ( 9 , 1 ) and ( βˆ’ 8 , π‘š ) are the direction vectors of two perpendicular straight lines, determine the value of π‘š .

  • A72
  • B βˆ’ 8 9
  • C βˆ’ 7 2
  • D 8 9

Q5:

In the square 𝐴 𝐡 𝐢 𝐷 with 𝐴 ( βˆ’ 2 , 3 ) and 𝐡 ( βˆ’ 8 , 9 ) , the diagonals are 𝐴 𝐢 and 𝐡 𝐷 . What is the slope of βƒ–     βƒ— 𝐡 𝐷 ?

  • A1
  • B βˆ’ 1
  • C0
  • D6

Q6:

Determine the slope of the straight line that makes an angle whose cosine is βˆ’ 3 4 with the positive π‘₯ -axis.

  • A βˆ’ √ 7 3
  • B βˆ’ 7 3
  • C √ 7 4
  • D βˆ’ 4 3

Q7:

In the figure below, find the slope of the line 𝐿 , and round the result to the nearest hundredth.

Q8:

If 𝐴 𝐡 𝐢 𝐷 is a parallelogram, where 𝐴 ( 8 , 2 ) and 𝐡 ( βˆ’ 4 , 7 ) , find the slope of βƒ–     βƒ— 𝐷 𝐢 .

  • A βˆ’ 5 1 2
  • B 1 2 5
  • C βˆ’ 1 2 5
  • D 5 1 2

Q9:

Given that β–³ 𝐴 𝐡 𝐢 is right angled at 𝐡 and that the coordinates of 𝐴 and 𝐡 are ( βˆ’ 3 , βˆ’ 8 ) and ( 3 , 0 ) , respectively, determine the slope of βƒ–     βƒ— 𝐡 𝐢 .

  • A βˆ’ 3 4
  • B 4 3
  • C0
  • D 3 4

Q10:

Find the slope of the straight line whose equation is 6 𝑦 = π‘Ž π‘₯ + 9 and passes through the point 𝐴 ( 7 , βˆ’ 2 ) .

  • A βˆ’ 1 2
  • B βˆ’ 3
  • C βˆ’ 1 2 7
  • D βˆ’ 2 7

Q11:

In this figure, the slope of βƒ–     βƒ— 𝐴 𝐡 is .

  • Anegative
  • Bzero
  • Cpositive
  • Dundefined

Q12:

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

Q13:

Find the slope of the given straight line.

  • A βˆ’ 1 7
  • B1
  • C 1 7
  • D7
  • E βˆ’ 7

Q14:

𝐿 𝑀 𝑁 is a right-angled triangle at 𝐿 where π‘š ∠ 𝑀 = 4 5 ∘ and the coordinates of 𝐿 and 𝑀 are 𝐿 ( 7 , βˆ’ 4 ) and 𝑀 ( βˆ’ 3 , βˆ’ 4 ) respectively. Find the coordinates of 𝑁 given the slope of 𝑀 𝑁 is 1.

  • A ( 7 , 6 )
  • B ( βˆ’ 3 , βˆ’ 1 4 )
  • C ( 7 , βˆ’ 1 4 )
  • D ( 1 7 , βˆ’ 4 )
  • E ( βˆ’ 3 , βˆ’ 4 )

Q15:

Use the graph to answer the following questions.

Determine the lengths of 𝐹 𝐺 , 𝐺 𝐻 , 𝐢 𝐷 , and 𝐷 𝐸 .

  • A 𝐹 𝐺 = 5 , 𝐺 𝐻 = 5 , 𝐢 𝐷 = 3 , 𝐷 𝐸 = 3
  • B 𝐹 𝐺 = 5 , 𝐺 𝐻 = 5 , 𝐢 𝐷 = 3 , 𝐷 𝐸 = 5
  • C 𝐹 𝐺 = 3 , 𝐺 𝐻 = 3 , 𝐢 𝐷 = 5 , 𝐷 𝐸 = 5
  • D 𝐹 𝐺 = 3 , 𝐺 𝐻 = 5 , 𝐢 𝐷 = 5 , 𝐷 𝐸 = 3
  • E 𝐹 𝐺 = 5 , 𝐺 𝐻 = 3 , 𝐢 𝐷 = 3 , 𝐷 𝐸 = 5

What is the ratio of 𝐺 𝐻 𝐹 𝐺 ?

What do you notice about the ratios 𝐺 𝐻 𝐹 𝐺 and 𝐷 𝐸 𝐢 𝐷 ?

  • AThey are not equal.
  • BThey are equal.

What do the ratios 𝐺 𝐻 𝐹 𝐺 and 𝐷 𝐸 𝐢 𝐷 represent?

  • Athe inverse of the slope of the line 𝐹 𝐸
  • Bthe slope of the line 𝐹 𝐸

Q16:

Which line has a slope that is greater than 1?

  • A a
  • B c
  • C b

Q17:

What is the gradient of a line passing through the points and ?

  • A1
  • B
  • C
  • D
  • E2

Q18:

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

  • Afalse
  • Btrue

Q19:

Which of the following characteristics does the line that passes through the points ( βˆ’ 7 , βˆ’ 6 . 7 5 ) , ( 3 , βˆ’ 1 4 . 2 5 ) , and ( βˆ’ 2 , βˆ’ 1 0 . 5 ) have?

  • Aa negative slope and a negative 𝑦 -intercept
  • B a positive slope and a positive 𝑦 -intercept
  • C a negative slope and a positive 𝑦 -intercept
  • D a positive slope and a negative 𝑦 -intercept

Q20:

What is the value of π‘₯ in the graph if the slope is equal to 0.7? Give your answer correct to two decimal places.

Q21:

A straight line has the equation 𝑦 = 4 π‘₯ βˆ’ 5 . What is the slope of the line?

Q22:

Given that a linear function contains the points (2,3) and (0,6), find the slope of the function and state whether it is increasing or decreasing.

  • A βˆ’ 1 . 5 , decreasing
  • B3, decreasing
  • C1.5, increasing
  • D2, decreasing

Q23:

Given that the slope of a straight line passing through the points ( 9 , βˆ’ 7 ) and ( βˆ’ 3 , π‘˜ ) is βˆ’ 5 1 2 , find the value of π‘˜ .
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