Practice Maths

Topic Review — Linear Relationships

Mixed Practice — L20 – L23

This review covers all lessons in the Linear Relationships topic: plotting, finding rules, gradient, and equations of lines. Try each question before checking your answers.

Review Questions

  1. Plotting and tables of values. Fluency

    1. Complete the table of values for y = 2x − 1 for x = 0, 1, 2, 3, 4.
    2. Complete the table of values for y = −3x + 9 for x = 0, 1, 2, 3.
    3. Which of these points lies on the line y = 4x − 5? Check each: (0, −5), (2, 3), (3, 8).
    4. A line passes through (0, −2) and (3, 4). List two more points on the same line.

  2. Finding linear rules. Fluency

    1. Find the rule y = mx + c for this table: x: 0, 1, 2, 3 / y: 7, 10, 13, 16.
    2. Find the rule y = mx + c for this table: x: 0, 2, 4, 6 / y: 3, −1, −5, −9.
    3. Find the rule for a line through (1, 5) and (3, 11).
    4. Write the rule for a line with gradient −4 and y-intercept 6.
    5. A line has gradient 3 and passes through (2, 8). Find its rule.

  3. Gradient. Understanding

    1. Find the gradient of the line through (−2, 3) and (4, −9).
    2. A line has gradient −2 and passes through (3, 4). Find the y-intercept.
    3. Which line is steeper: y = 5x − 1 or y = −8x + 3? Explain.
    4. Three points are: P(0, −3), Q(2, 5), R(4, 13). Are P, Q, and R collinear? Show working.
    5. A ramp rises 0.9 m over a horizontal distance of 4.5 m. What is its gradient?
    6. Find the missing coordinate: gradient = 3, points (1, 2) and (4, ?).

  4. Equations of lines. Understanding

    1. Write the equation in y = mx + b form for: gradient = −3, y-intercept = 5.
    2. Identify m and b: y = ⅔x − 7.
    3. Find the equation of the line through (0, 4) and (3, −2).
    4. Find the equation of the line with the same gradient as y = 5x + 2 and y-intercept 9.
    5. Two lines are y = −x + 8 and y = −x − 3. Describe the relationship between these lines.
    6. A line crosses the x-axis at 5 and the y-axis at 10. Write its equation.

  5. Mixed linear relationships problem solving. Problem Solving

    1. A car rental company charges $45 per day plus a $30 booking fee.
      1. Write an equation for total cost C in terms of days d.
      2. Find the cost for 5 days.
      3. How many days can you rent if your budget is $210?
    2. A water tank holds 800 litres when full and drains at 50 litres per hour. Write an equation for the volume V after t hours. After how many hours is the tank a quarter full?
    3. Line P has equation y = 3x + 1 and Line Q passes through (−1, −5) and (2, 4). Do Lines P and Q intersect? If so, are they the same line, parallel, or different?
    4. A table of values for a linear relationship is: x: −1, 0, 1, 2, 3 / y: −7, −4, −1, 2, 5. Find the rule, then find x when y = 20.
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