How would you write an equation of the line that passes through another point?
<< equation of the line that passes throught point P and is parallel to the line with the given equation: ex: P(-2,0); y=-1/2x+6 >> The slope of the line = -1/2 (from the equation y = -1/2x + 6) and if the line passing through P(-2,0) is parallel to the given line then its slope must also be equal to -1/2 (since lines that are parallel have the same slopes) slope = m = delta y/delta x where delta y = change in y-coordinates delta x = change in x-coordinates Therefore, -1/2 = (y – 0)/(x – -2) = y/(x + 2) Simplifying, -(x + 2) = 2y -x – 2 = 2y Solving for “y”, y = (-1/2)x – 1 << Equation of the line that passes through point P and is perpendicular to the line with the given equation: ex: P(5,20); y=1/2x+8 >> The slope of the line is 1/2 and the slope of the line perpendicular to the given line is equal to -2 (since the slope of a line perpendicular to a given line is equal to the negative reciprocal).
