Write Equations of Parallel and Perpendicular Lines
The converse of a conditional statement interchanges the hypothesis and conclusion Parallel Lines If two lines have the same slope, then they are parallel If two lines are parallel, then they have the same slope
Example Write an equation of the line that passes through (-3,-5) and is parallel to y=3x-1 Step 1 Find the slope. m= 3 Step 2 Write the equation using y=m(x-h)+k y = 3(x-(-3))-5 y=3x+9-5 Y=3x+4
Example 2 Write an equation of the line that passes through (-2,11) and is parallel to y=-x+5 Step 1 Find the slope. m= -1 Step 2 Write the equation using y=m(x-h)+k y = -1(x-(-2))+11 y=-x-2+11 Y=-x+9
Perpendicular Lines Two lines are perpendicular if they intersect to form right angles. Horizontal and vertical lines are perpendicular to each other. Perpendicular Lines If two lines have slopes that are negative reciprocals, then they are perpendicular If two lines are perpendicular, then their slopes are negative reciprocals
Example 3 Determine Whether the Lines are Parallel or Perpendicular Line a: y=5x-3 Line b: x+5y=2 Line c: -10y-2x=0 Line b: x+5y=2 Line c: -10y-2x=0 5y=-x+2 -10y=2x y= Lines b and c have slopes of so they are parallel. Line a has a slope of 5, so it is perpendicular to lines b and c.
Example 4 Determine Whether the Lines are Parallel or Perpendicular Line a: 2x+6y=-3 Line b: y=3x-8 Line c: -1.5y+4.5x=6 Line a: 6y=-2x-3 Line c: -1.5y=-4.5x+6 Lines b and c have the same slopes so they are parallel. The slope of line a is the negative reciprocal of the slope of line b and c, so it is perpendicular to lines b and c.
Example 5 Determine whether the lines are perpendicular Line a: 3y=2x-1 Line b: 2y=-3x+21 Line a: Line b:
Example 6 Determine whether the lines are perpendicular line a: y=4x-2 line b:-4y-x=0 line b: -4y=x Lines a and b are perpendicular
Example 7 Write an equation of the line that passes through (4,-5) and is perpendicular to the line y=2x+3. Step 1: The slope must be Step 2: Write the equation in y=m(x-h)+k form