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Questions and Answers
Quelle est l'équation réduite d'une ligne verticale?
Comment peut-on déterminer l'équation d'une ligne passant par deux points?
Quelle est la condition pour que deux lignes soient parallèles?
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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