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Worksheet: Point-Slope Form

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 1
  • Bline 2

Q2:

Which line has a slope that is greater than 1?

  • A b
  • B a
  • C c

Q3:

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

Q4:

is a right triangle at where and the coordinates of and are and respectively. Find the coordinates of given the slope of is 1.

  • A
  • B
  • C
  • D
  • E

Q5:

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

  • Atrue
  • Bfalse

Q6:

In the square with and , the diagonals are and . What is the gradient of ?

  • A6
  • B
  • C0
  • D1

Q7:

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

Q8:

What is the value of 𝑦 so that 𝐴 ( βˆ’ 4 , βˆ’ 8 ) , 𝐡 ( 2 , βˆ’ 2 ) , and 𝐢 ( βˆ’ 7 , 𝑦 ) are collinear?

Q9:

What is the value of 𝑦 so that 𝐴 ( 2 , βˆ’ 6 ) , 𝐡 ( 4 , βˆ’ 3 ) , and 𝐢 ( 7 , 𝑦 ) are collinear?

Q10:

Given that the gradient of a straight line passing through the points and is , find the value of .

  • A5
  • B2
  • C
  • D

Q11:

Determine the gradient of the straight line that makes an angle whose cosine is with the positive -axis.

  • A
  • B
  • C
  • D

Q12:

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?

  • A a positive slope and a negative 𝑦 -intercept
  • B a positive slope and a positive 𝑦 -intercept
  • C a negative slope and a positive 𝑦 -intercept
  • Da negative slope and a negative 𝑦 -intercept

Q13:

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.

  • A2, decreasing
  • B3, decreasing
  • C1.5, increasing
  • D βˆ’ 1 . 5 , decreasing

Q14:

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.

Q15:

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

Q16:

In the figure below, find the gradient of the line , and approximate the result to the nearest hundredth, if needed.

  • A0.87
  • B1.15
  • C0.75
  • D
  • E

Q17:

If is a parallelogram, where and , find the gradient of .

  • A
  • B
  • C
  • D

Q18:

Given that is right triangle at and that the coordinates of and are and , respectively, determine the slope of .

  • A
  • B
  • C0
  • D

Q19:

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

Q20:

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

  • Aundefined
  • Bzero
  • Cpositive
  • Dnegative

Q21:

Given that the gradient of the line passing through , , and is , find the values of and .

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

Q22:

Find the gradient of the straight line whose equation is and passes through the point .

  • A
  • B
  • C
  • D

Q23:

Find the gradient of the given straight line.

  • A
  • B
  • C7
  • D
  • E1