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Questions and Answers

Quelle est l'équation réduite d'une ligne verticale?

  • y = mx + p
  • x = k (correct)
  • y = kx + p
  • x = mp + k

    • Comment peut-on déterminer l'équation d'une ligne passant par deux points?

  • En utilisant la formule pour la pente et les coordonnées des deux points.
  • En utilisant la formule pour la pente et les coordonnées d'un des points. (correct)
  • En utilisant la formule pour la distance entre deux points.
  • En utilisant la formule pour l'aire d'un triangle formé par les deux points et l'origine

    • Quelle est la condition pour que deux lignes soient parallèles?

  • Leurs coefficients doivent être égaux.
  • Leurs pentes doivent être égales. (correct)
  • Leurs coefficients doivent satisfaire ab' - ba' = 0.
  • Leurs pentes doivent satisfaire ab' - ba' = 0.

    • Study Notes

    • A non-vertical line has an equation of the form y = mx + p and a vertical line has an equation of the form x = k.
    • The equation y = mx + p or x = k is called the reduced equation of the line.
    • The coefficient m is called the slope or gradient of the line.
    • The equation ax + by + c = 0 is the Cartesian equation of a line.
    • Any line has an equation of the form ax + by + c = 0.
    • Two lines are parallel if and only if their slopes are equal (for reduced equations) or if their coefficients satisfy ab' - ba' = 0 (for Cartesian equations).
    • The equation of a line passing through two points can be determined using the formula for slope and the coordinates of one of the points.
    • To solve a system of two equations graphically, plot the equations as lines and determine if they intersect (one solution), are parallel (no solution), or coincide (infinitely many solutions).
    • The reduced equation is useful for non-vertical lines, while the Cartesian equation is more general.
    • The slope of a line is a measure of its steepness or inclination.

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