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Parallel and Perpendicular Lines Calculator

Give a line and a point, and get the equation of the line through that point running either parallel or at right angles to it. Parallel keeps the gradient identical; perpendicular flips it upside down and changes its sign. The intercept is then found by substituting the point in.

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Method, Step by Step

    Worked Example

    Find the line perpendicular to y = 2x + 1 passing through (4, 3).

    1. Perpendicular gradients multiply to −1, so flip 2 and change the sign:−1 ÷ 2 = −0.5
    2. Put (4, 3) into y = −0.5x + c:3 = −0.5 × 4 + c
    3. So c = 3 − (−2) = 5, and the line is y = −0.5x + 5

    Answer: y = −0.5x + 5

    Try These Yourself

    What gradient is perpendicular to 3?Show answerHide answer

    Answer: −13

    Flip it and change the sign.

    Find the line parallel to y = 4x − 2 through (0, 7).Show answerHide answer

    Answer: y = 4x + 7

    Same gradient, and the point gives c straight away.

    Are y = 2x + 1 and y = 2x − 6 parallel?Show answerHide answer

    Answer: Yes

    Identical gradients, different intercepts.