# Lesson Worksheet: Slopes and Intercepts of Linear Functions Mathematics • 8th Grade

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

Q1:

What is the -intercept of the function ?

Q2:

What is the slope of the function ?

Q3:

Determine the slope and -intercept of the line .

• ASlope = 1, intercepted part = 3
• BSlope = , intercepted part = 3
• CSlope = , intercepted part = 1
• DSlope = 3, intercepted part = 1

Q4:

What is the slope of the function ?

Q5:

Which of the following pairs has the same slope as that of ?

• 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)

Q6:

What is the slope of the line represented by the equation ?

Q7:

The graph of the equation is a straight line.

What is the slope of the line?

What is the -intercept of the line?

Q8:

What is the slope of the line represented by the equation ?

Q9:

What is the slope of the linear function ?

Q10:

Given that the straight line passing through the points and is parallel to the -axis, determine the value of .

Q11:

Determine the slope and -intercept of the line .

• ASlope = 5, intercepted part = 1
• BSlope = , intercepted part = 1
• CSlope = , intercepted part =
• DSlope = 1, intercepted part = 5

Q12:

Determine the slope and -intercept of the line .

• ASlope = , intercepted part = 6
• BSlope = , intercepted part = 6
• CSlope = , intercepted part =
• DSlope = 6, intercepted part = 8

Q13:

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

 𝑥-value 𝑦-value −1 2 3 2 11 14

Q14:

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

 𝑥 𝑦 5 10 15 20 −2 1 4 7
• A,
• B,
• C,
• D,
• E,

Q15:

The graph below represents a relation between the time in hours and the amount of fuel in a car tank 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 liters per hour.
• BThe amount of remaining fuel is liters and the amount of fuel consumed is liters per hour.
• CThe amount of remaining fuel is 24 liters and the amount of fuel consumed is liters per hour.
• DThe amount of remaining fuel is 24 liters and the amount of fuel consumed is liters per hour.

Q16:

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

• A3
• B0
• C
• D
• E

Q17:

The graph below represents the movement of a bicycle measured from a constant point. Calculate the velocity of the bicycle during the first 4 hours and during the next 5 hours. • AThe first velocity is 75 km/h, and the second velocity is km/h.
• BThe first velocity is km/h, and the second velocity is km/h.
• CThe first velocity is 450 km/h, and the second velocity is km/h.
• DThe first velocity is km/h, and the second velocity is km/h.

Q18:

A farmer decided to dig a well. The graph represents the time in hours to dig the well against the depth of the well in metres . 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. • A15 m, 40 h, m/h
• B40 m, 18 h, m/h
• C15 m, 18 h, m/h
• D15 m, 18 h, 5 m/h

Q19:

The graph shows the relation between time , and pages remaining of a book being read . 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 , 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.

Q20:

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. • A4 km/h, km/h
• B km/h, km/h
• C4 km/h, 5 km/h
• D km/h, km/h

Q21:

A woman drove 40 km to city . Then, she drove to city at a constant speed, as shown in the figure. Find the speed of the car during her journey between and . At what distance is she from her starting point at hours? • A75 km/h, 145 km
• B35 km/h, 145 km
• C35 km/h, 105 km
• D75 km/h, 105 km

Q22:

The figure shows the relation between the amount of fuel left in a tank and the time in hours. Find the greatest capacity of the tank and how long it will take to be emptied. • A60 liters, after 30 hours
• B60 liters, after 30 hours
• C30 liters, after 60 hours
• D30 liters, after 30 hours
• E2 liters, after 30 hours

Q23:

The graph shows the distance travelled over time by a car. Find the average velocity of the car for the first four hours and then over the next three hours. • AThe first velocity is km/h, and the second velocity is km/h.
• BThe first velocity is km/h, and the second velocity is km/h.
• CThe first velocity is km/h, and the second velocity is km/h.
• DThe first velocity is 50 km/h, and the second velocity is km/h.

Q24:

The graph shows the distance a car traveled over time. Given that the car moved at a constant speed, determine the speed the car was moving at. • A20 km/h
• B60 km/h
• C100 km/h
• D70 km/h
• E80 km/h

Q25:

Using the fact that the slope is the same between any two distinct points on a nonvertical line in the coordinate plane, calculate the value of in the graph. • A5
• B7
• C2
• D
• E3