Worksheet: Slopes and Intercepts of Linear Functions

In this worksheet, we will practice identifying slopes and intercepts of linear functions both algebraically and graphically.

Q1:

What is the 𝑦-intercept of the function 3𝑦=15π‘₯+18?

Q2:

What is the slope of the function 2𝑦=4π‘₯βˆ’1?

Q3:

Determine the slope and 𝑦-intercept of the line βˆ’3𝑦=3βˆ’π‘₯.

  • ASlope = 1, intercepted part = 3
  • BSlope = βˆ’13, intercepted part = 3
  • CSlope = 13, intercepted part = 1
  • DSlope = 3, intercepted part = 1

Q4:

Which of the following lines has intercepts (0,3) and (βˆ’2,0)?

  • A 6 𝑦 βˆ’ 4 π‘₯ = 4
  • B 6 𝑦 βˆ’ 4 π‘₯ = 1 2
  • C 4 𝑦 βˆ’ 6 π‘₯ = 1 2
  • D 4 𝑦 βˆ’ 6 π‘₯ = 4
  • E 6 𝑦 + 4 π‘₯ = 1 2

Q5:

List the π‘₯- and 𝑦-intercepts of the line 2π‘₯βˆ’3𝑦=7.

  • A ο€Ό 0 , 7 3  , ο€Ό 7 2 , 0 
  • B ο€Ό 0 , 7 3  , ο€Ό βˆ’ 7 2 , 0 
  • C ο€Ό 0 , βˆ’ 7 2  , ο€Ό 7 3 , 0 
  • D ο€Ό 0 , βˆ’ 7 3  , ο€Ό βˆ’ 7 2 , 0 
  • E ο€Ό 0 , βˆ’ 7 3  , ο€Ό 7 2 , 0 

Q6:

What is the slope of the function 𝑦=8π‘₯βˆ’3?

Q7:

Which of the following pairs has the same slope as that of 𝑦=6π‘₯βˆ’4?

  • A(3, 15), (4, 20)
  • B(5, 10), (6, 12)
  • C(2, 8), (4, 20)
  • D(4, 16), (2, 8)
  • E(3, 9), (2, 6)

Q8:

What is the slope of the line represented by the equation 𝑦=6π‘₯βˆ’7?

Q9:

The graph of the equation 𝑦=4π‘₯+2 is a straight line.

What is the slope of the line?

What is the 𝑦-intercept of the line?

Q10:

The graph of the equation 4π‘₯βˆ’3𝑦=24 is a straight line.

What is the π‘₯-intercept of the line?

What is the 𝑦-intercept of the line?

What is the slope of the line?

  • A 1 8
  • B 4 3
  • C 1 3
  • D 3 4
  • E 1 6

Q11:

What is the slope of the line represented by the equation 𝑦=βˆ’3π‘₯+1?

Q12:

What is the slope of the linear function 𝑦=3π‘₯+2?

Q13:

Given that the straight line passing through the points (3π‘₯,βˆ’3) and (15,0) is parallel to the 𝑦-axis, determine the value of π‘₯.

Q14:

Determine the slope and 𝑦-intercept of the line 4𝑦=1βˆ’5π‘₯.

  • ASlope = 5, intercepted part = 1
  • BSlope = 54, intercepted part = 1
  • CSlope = βˆ’54, intercepted part = 14
  • DSlope = 1, intercepted part = 5

Q15:

Determine the slope and 𝑦-intercept of the line βˆ’7𝑦=6+8π‘₯.

  • ASlope = βˆ’8, intercepted part = 6
  • BSlope = 87, intercepted part = 6
  • CSlope = βˆ’87, intercepted part = 67
  • DSlope = 6, intercepted part = 8

Q16:

What is the initial value (𝑦-intercept) of the linear function represented by the given table?

π‘₯ -value βˆ’ 1 2 3
𝑦 -value 2 11 14

Q17:

The points in the table belong to the same line. Find the slope and the 𝑦-intercept of the line.

π‘₯ 5 10 15 20
𝑦 βˆ’ 2 1 4 7
  • Aslope=53, 𝑦-intercept =253
  • Bslope=35, 𝑦-intercept =253
  • Cslope=35, 𝑦-intercept =βˆ’5
  • Dslope=53, 𝑦-intercept =βˆ’5
  • Eslope=110, 𝑦-intercept =1

Q18:

The graph below represents a relation between the time 𝑑 in hours and the amount of fuel in a car tank 𝑦 in liters. Determine the amount of fuel remaining after 15 hours of driving and the amount of fuel consumed per hour.

  • AThe amount of remaining fuel is 36 liters and the amount of fuel consumed is 225 liters per hour.
  • BThe amount of remaining fuel is 35 liters and the amount of fuel consumed is 225 liters per hour.
  • CThe amount of remaining fuel is 24 liters and the amount of fuel consumed is 225 liters per hour.
  • DThe amount of remaining fuel is 24 liters and the amount of fuel consumed is 512 liters per hour.

Q19:

What is the slope of the line that passes through the origin and the point (2, 5)?

  • A3
  • B0
  • C 5 2
  • D 2 5
  • E βˆ’ 3

Q20:

The graph below represents the movement of a bicycle measured from a constant point. Calculate the velocity of the bicycle during the first four hours and during the next five hours.

  • AThe first velocity is 75 km/h, and the second velocity is βˆ’20 km/h.
  • BThe first velocity is 11212 km/h, and the second velocity is βˆ’79 km/h.
  • CThe first velocity is 450 km/h, and the second velocity is βˆ’350 km/h.
  • DThe first velocity is 11212 km/h, and the second velocity is βˆ’3889 km/h.

Q21:

A farmer decided to dig a well. The graph represents the time in hours to dig the well (𝑑) against the depth of the well in metres (𝑑). Find the depth of the well before digging, the time it took to finish digging, and the average digging depth per hour during the first six hours.

  • A 15 m, 40 h, 1 5 m/h
  • B 40 m, 18 h, 5 2 m/h
  • C 15 m, 18 h, 5 2 m/h
  • D 15 m, 18 h, 5 m/h

Q22:

The graph shows the relation between time 𝑑, and pages remaining of a book being read 𝑦. Assuming the relation continues to be linear, find the number of pages in the book, the number of pages read per hour, and the number of hours it will take to finish the book.

  • AThe number of pages in the book is 6, the number of pages read per hour is 120, and it will take 120 hours to finish the book.
  • BThe number of pages in the book is 120, the number of pages read per hour is 20, and it will take 6 hours to finish the book.
  • CThe number of pages in the book is 120, the number of pages read per hour is 10, and it will take 6 hours to finish the book.
  • DThe number of pages in the book is 6, the number of pages read per hour is 20, and it will take 120 hours to finish the book.

Q23:

The distance-time graph plots a cyclist’s journey from point A to B and then back again, where time is measured in hours and distance in kilometres. Find the average speed on the cyclist’s outward journey and the average speed on the return journey.

  • A 4 km/h, 1 2 1 2 km/h
  • B 1 4 km/h, 3 3 4 km/h
  • C 4 km/h, 5 km/h
  • D 1 4 km/h, 1 5 km/h

Q24:

A woman drove 40 km to city 𝐴. Then, she drove to city 𝐡 at a constant speed, as shown in the figure. Find the speed of the car during her journey between 𝐴 and 𝐡. At what distance is she from her starting point at 𝑑=3 hours?

  • A 75 km/h, 145 km
  • B 35 km/h, 145 km
  • C 35 km/h, 105 km
  • D 75 km/h, 105 km

Q25:

The figure shows the relation between the amount of fuel left in a tank (𝑦) and the time in hours(𝑑). Find the greatest capacity of the tank and how long it will take to be emptied.

  • A 60 liters, after 30 hours
  • B 60 liters, after 30 hours
  • C 30 liters, after 60 hours
  • D 30 liters, after 30 hours
  • E 2 liters, after 30 hours

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