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Worksheet: Positive, Negative, and Undefined Slopes

Q1:

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

Q2:

The graph shows the capital of a company over 8 years. Determine the slope of the line which represents the increase in capital in the first three years.

  • A βˆ’ 1 0 3
  • B 3 1 0
  • C βˆ’ 3 1 0
  • D 1 0 3

Q3:

Consider the four points 𝐴 ( 1 , 2 ) , 𝐡 ( 6 , 0 ) , 𝐢 ( βˆ’ 1 , βˆ’ 2 ) , and 𝐷 ( 3 , βˆ’ 4 ) .

Work out the slope of the line βƒ–     βƒ— 𝐴 𝐡 .

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

Work out the slope of the line βƒ–     βƒ— 𝐢 𝐷 .

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

Are the two lines parallel?

  • AYes
  • BNo

Q4:

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 an obtuse angle.
  • CIt is a zero angle.
  • DIt is an acute angle.

Q5:

Line 𝐿 passes through points ( βˆ’ 1 , 2 ) and ( 2 , 3 ) , and line 𝑀 passes through points ( βˆ’ 1 , βˆ’ 1 ) and ( 5 , 1 ) .

Work out the slope of line 𝐿 .

  • A1
  • B3
  • C βˆ’ 3
  • D 1 3
  • E βˆ’ 1 3

Work out the slope of line 𝑀 .

  • A 1 3
  • B βˆ’ 3
  • C0
  • D3
  • E 1 2

Are the two lines parallel?

  • ANo
  • BYes

Q6:

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

  • Aundefined
  • Bnegative
  • Cpositive
  • Dzero

Q7:

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

  • Anegative
  • Bpositive
  • Czero
  • Dundefined

Q8:

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

  • Anegative
  • Bundefined
  • Czero
  • Dpositive

Q9:

What is the slope of the line in the given graph?

Q10:

What is the slope of the line passing through the points ο€Ό 2 , 2 3  and ( 6 , 2 ) ?

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

Q11:

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

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

Q12:

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

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

Q13:

Calculate the slope of the line in the graph.