Parallel and Parallel and Perpendicular Perpendicular

LinesLinesObjectives: Define parallel lines.Objectives: Define parallel lines.Find equations of parallel lines.Find equations of parallel lines.

Define perpendicular linesDefine perpendicular linesFind equations of perpendicular lines.Find equations of perpendicular lines.

Parallel LinesParallel Lines• Slopes of parallel lines are equal.

• Recall the steps of finding an equation of a line.– Find slope– Find the y-intercept– Write the equation

– This is the same process when working with parallel and perpendicular lines.

Find an equation of a line Find an equation of a line passing through (-2,5) that is passing through (-2,5) that is

parallel to parallel to 3x + 2y = 93x + 2y = 9

• Find slope:– Get y by itself in the given equation

2y = 9 – 3x y = 9/2 – 3/2 x slope=-3/2

• Find y-intercept:– Use a slope of -3/2 since the lines are parallely = -3/2 x + b 5 = -3/2 (-2) + b 5 = 3 + b2 = b

• Write equation:y = -3/2 x + 2

Perpendicular LinesPerpendicular Lines• Perpendicular lines have negative

reciprocal slopes.• If a line has a slope of -1/2 the

perpendicular line would have a slope of 2.• If a line has a slope of 5/6 the

perpendicular line would have a slope of -6/5

• What would be the slope of a line perpendicular to a line with a slope of -7?

1/7

Find the equation of the line Find the equation of the line passing through (-1,3) that is passing through (-1,3) that is perpendicular to 3x – 2y = 8.perpendicular to 3x – 2y = 8.

1. Find slope1. Get y by itself: -2y = 8 – 3x y = -4 +

3/2 x2. Slope is 3/2 so perpendicular slope is -

2/3

2. Find y-intercept1. y = -2/3 x + b 3 = (-2/3)(-1) + b

3 = 2/3 + b 3 – 2/3 = b 7/3 = b

3. Write equationy = -2/3 x + 7/3

Review concepts learnedReview concepts learned• Parallel lines have equal slope• Perpendicular lines have negative

reciprocal slopes.• To find an equation of a line

– Find slope– Find y-intercept– Write equation

AssignmentAssignment• Page 197• #7, 11, 13, 17, 21, 23, 25, 29, 33, 37