Skip to main content
    Achieve Academy
    Back to Resources

    Graphs

    Revision notes · Maths

    Formula SheetPractice bookletsFlashcards
    Tier
    Practise questions
    Lesson step 1 of 4Linear Graphs

    Linear Graphs

    Every straight line can be written in the form y = m𝑥 + c, where:

    m = the gradient (how steep the line is)

    c = the y-intercept (where it crosses the y-axis)

    The gradient measures the rate of change — how much y changes for each unit increase in 𝑥.

    Gradient from two points: m = (y2 − y1) / (𝑥2 − 𝑥1)
    This is often described as 'rise over run'.

    Two lines are parallel if they have the same gradient. (Perpendicular lines are covered in 'Parallel & Perpendicular Lines'.)

    To find the equation of a line, you need:

    The gradient AND one point, OR

    Two points (find the gradient first, then use one point)

    1 / 13

    Key Terms

    Gradient
    How steep a line is — it tells you how much the line goes up (or down) for every 1 step to the right.
    y-intercept
    The point where the graph crosses the vertical axis (the y-axis) — it's the value of y when 𝑥 = 0.
    Turning point
    The highest or lowest point on a curve — where it changes direction from going up to going down (or vice versa).
    Tangent (to a curve)
    A straight line that just touches a curve at one point without cutting through it — you draw one to estimate the steepness at that point.