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About Linear Functions & Graphs — Class 8 IB

Graph linear functions, find slope and intercepts, and interpret graphs in context. This topic is part of the IB Class 8 mathematics syllabus (chapter: Unit 3). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Linear Functions & Graphs — solved examples for Class 8 IB

Example 1easy

What is the slope of the line \(y = 3x + 2\)?
  1. A)2
  2. B)3
  3. C)5
  4. D)1

Step-by-step solution

  1. Compare with \(y = mx + c\). The coefficient of \(x\) is the slope.
    m=3m = 3

Answer: 3

Example 2medium

Find the slope of the line passing through the points (2, 5) and (6, 13).
  1. A)\(\frac{1}{2}\)
  2. B)2
  3. C)4
  4. D)8

Step-by-step solution

  1. Apply the slope formula.
    m=13−56−2=84=2m = \frac{13 - 5}{6 - 2} = \frac{8}{4} = 2

Answer: 2

Example 3hard

Find the equation of the line passing through (2, -1) and (5, 8).
  1. A)\(y = 3x - 7\)
  2. B)\(y = 3x + 7\)
  3. C)\(y = -3x + 5\)
  4. D)\(y = 3x - 1\)

Step-by-step solution

  1. Find slope.
    m=8−(−1)5−2=93=3m = \frac{8-(-1)}{5-2} = \frac{9}{3} = 3
  2. Use point (2, -1).
    −1=3(2)+c⇒c=−7-1 = 3(2) + c \Rightarrow c = -7
  3. Equation:
    y=3x−7y = 3x - 7

Answer: \(y = 3x - 7\)

Practice questions on Linear Functions & Graphs

  1. Q1.easy

    What is the y-intercept of the line \(y = 5x - 4\)?
    1. A)5
    2. B)-4
    3. C)4
    4. D)-5
    Show answer

    Answer: -4

    Hint: The y-intercept is the constant term in \(y = mx + c\).

  2. Q2.easy

    Which of the following is a linear function?
    1. A)\(y = x^2 + 1\)
    2. B)\(y = 2x - 3\)
    3. C)\(y = \frac{1}{x}\)
    4. D)\(y = \sqrt{x}\)
    Show answer

    Answer: \(y = 2x - 3\)

    Hint: A linear function has the form \(y = mx + c\) with no exponents on \(x\).

  3. Q3.easy

    If a line passes through the origin with slope 2, what is its equation?
    1. A)\(y = 2\)
    2. B)\(y = 2x\)
    3. C)\(y = x + 2\)
    4. D)\(x = 2y\)
    Show answer

    Answer: \(y = 2x\)

    Hint: Passing through the origin means the y-intercept is 0.

  4. Q4.medium

    Write the equation of a line with slope 3 and y-intercept -2.
    1. A)\(y = -2x + 3\)
    2. B)\(y = 3x - 2\)
    3. C)\(y = 3x + 2\)
    4. D)\(y = -2x - 3\)
    Show answer

    Answer: \(y = 3x - 2\)

    Hint: Use the form \(y = mx + c\) with \(m = 3\) and \(c = -2\).

  5. Q5.medium

    Find the equation of the line passing through (0, 4) with slope \(-\frac{1}{2}\).
    1. A)\(y = -\frac{1}{2}x + 4\)
    2. B)\(y = 4x - \frac{1}{2}\)
    3. C)\(y = \frac{1}{2}x + 4\)
    4. D)\(y = -\frac{1}{2}x - 4\)
    Show answer

    Answer: \(y = -\frac{1}{2}x + 4\)

    Hint: The point (0, 4) tells us the y-intercept is 4.

  6. Q6.medium

    Rewrite \(2x + y = 6\) in slope-intercept form.
    1. A)\(y = 2x + 6\)
    2. B)\(y = -2x + 6\)
    3. C)\(y = 2x - 6\)
    4. D)\(y = -2x - 6\)
    Show answer

    Answer: \(y = -2x + 6\)

    Hint: Isolate y by moving the x term to the other side.

  7. Q7.hard

    Find the equation of a line perpendicular to \(y = 2x + 3\) passing through (4, 1).
    1. A)\(y = -\frac{1}{2}x + 3\)
    2. B)\(y = 2x - 7\)
    3. C)\(y = -\frac{1}{2}x - 1\)
    4. D)\(y = -2x + 9\)
    Show answer

    Answer: \(y = -\frac{1}{2}x + 3\)

    Hint: The perpendicular slope is the negative reciprocal of 2.

  8. Q8.hard

    A line passes through (-3, 7) and is parallel to \(y = -4x + 2\). Find its equation.
    1. A)\(y = -4x - 5\)
    2. B)\(y = -4x + 5\)
    3. C)\(y = 4x + 19\)
    4. D)\(y = -4x - 19\)
    Show answer

    Answer: \(y = -4x - 5\)

    Hint: Parallel lines have the same slope.

  9. Q9.hard

    Where do the lines \(y = x + 2\) and \(y = -x + 6\) intersect?
    1. A)(2, 4)
    2. B)(4, 2)
    3. C)(3, 3)
    4. D)(1, 3)
    Show answer

    Answer: (2, 4)

    Hint: Set the two equations equal to each other.

These are 9 of the 60 questions available for Linear Functions & Graphs. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.