MathsFreePrintable

Linear Relationships Plotting Worksheet

A free maths worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.

Download now

Name:Date:

Linear Relationships Plotting Worksheet

Complete each task. Show working for calculations and use a ruler for straight lines.

Tables and Linear Rules

1.For the rule y = 4x − 1, complete the y-values when x = −2, −1, 0, 1, 2. Then write the four first differences.

2.Are the values in the previous table a linear relationship? Give a reason based on the first differences.

3.Use y = −3x + 7 to complete the y-values for x = 0, 1, 2, 3, 4.

4.For y = 0.75x + 2, find y when x = −4, 0, 4, 8.

5.Which set of values is linear? Choose one and explain briefly. A: x = 0, 1, 2, 3; y = 1, 2, 4, 8. B: x = 0, 1, 2, 3; y = −2, 1, 4, 7. C: x = 0, 1, 2, 3; y = 0, 1, 4, 9.

6.For y = 2x − 5, complete the y-values at x = −1, 0, 1, 2, 3. Write the first differences and state whether the relationship is linear.

Plotting and Finding Equations

7.Plot the points for y = 4x − 1 when x = −2, −1, 0, 1, 2. Join them with a straight line.

8.For the line y = 4x − 1, state its y-intercept and gradient.

9.Plot (−2, 5), (0, 1), (2, −3) and (4, −7), then write the rule for the line.

10.A straight line passes through (0, −3) and (3, 6). Find its equation in the form y = mx + b.

11.Find the equation of the line through (2, 1) and (5, 10).

12.Match each set of coordinates to its rule: (0, 2), (1, 5), (2, 8); (0, 0), (1, −2), (2, −4); (0, 5), (1, 3), (2, 1); (0, −4), (1, 0), (2, 4). Rules: y = 3x + 2; y = −2x; y = −2x + 5; y = 4x − 4.

(0, 2), (1, 5), (2, 8)
(0, 0), (1, −2), (2, −4)
(0, 5), (1, 3), (2, 1)
(0, −4), (1, 0), (2, 4)

y = −2x
y = 3x + 2
y = 4x − 4
y = −2x + 5

Linear Relationships in Context

13.A bicycle hire service charges a fixed $18 fee plus $7 for each hour hired. Write a rule for the cost C after h hours, calculate the cost for 5 hours, and find the number of hours for a $60 hire.

14.A delivery service charges $4.50 as a booking fee and $1.80 per kilometre. Write a rule for a trip of d kilometres, calculate the charge for 10 km, and find the distance travelled for a $18.90 charge.

15.A 420-litre rainwater tank loses 12 litres each minute. Write a rule for the amount W remaining after t minutes, find the amount left after 15 minutes, and calculate when it will be empty.

16.A community art course has a $45 enrolment fee and costs $32 per month. Write a rule for the total cost T after m months and complete the totals for 0, 2, 4, 6 and 8 months.

Challenge

17.Which line is steepest? Select the line with the greatest gradient magnitude: y = 6x − 1, y = −8x + 4, or y = 3x + 9.

y = 6x − 1
y = −8x + 4
y = 3x + 9

18.A line has gradient 4 and passes through (−1, 3). Find its equation.

19.Two lines meet at (3, 10). One line is y = 2x + 4. A second line passes through (0, 1) and the meeting point. Find the equation of the second line.

20.When x increases by 3, y decreases by 12. The line passes through (2, 5). Find its equation.

21.A temperature of 0°C is 32°F, and 100°C is 212°F. Find the linear rule for Fahrenheit F in terms of Celsius C, then convert 30°C to Fahrenheit and 86°F to Celsius.

22.Explain how constant first differences in a table can help you decide whether a relationship is linear.