EQUATIONS OF LINES Parallel and Perpendicular Lines

Equations of Lines  We can also write equations of lines given other information.  Remember from geometry:  Parallel lines have the same slope.  Perpendicular lines have slopes that are opposite reciprocals.  Opposite reciprocal: if the slope is 3, the opposite reciprocal is -1/3.

Equations of Lines  Write the equation of the line that passes through (4,2) and is parallel to y=2x + 4.  If the lines are parallel, the slopes are the same.  The slope of the new line is m=2.  Now just like before, solve for “b”.  2 = 2(4) + b  2 = 8 + b  b = -6  So,…….  y = 2x - 6

Equations of Lines  Write the equation of the line that passes through (4,7) and is perpendicular to y = -2x + 9.  The new slope is m = ½ (opposite reciprocal)  Now finish like all of the other problems…..  7 = ½(4) + b  7 = 2 + b  b = 5  y = 1/2x + 5

Equations of lines  Your turn…… 1. Write the equation of a line that passes through the point (-2,-3) and is parallel to y=4x – y = 4x Write the equation of a line that passes through the point (7,1) and is perpendicular to y=4x y = -1/4x + 11/4