slopes of parallel and perpendicular lines (3.6) objective: to relate slope of parallel and...

Slopes of Parallel and Perpendicular Lines (3.6)Objective: To relate slope of parallel and perpendicular lines, and to write equations of parallel and perpendicular lines

Parallel Lines have the SAME slope

Perpendicular Lineshave OPPOSITERECIPROCAL

slopes

Slopes of Parallel Lines Slopes of parallel lines are equal =

Any 2 vertical lines are parallel; any 2 horizontal lines are parallel

Test whether 2 non-vertical or non-horizontal lines are // by comparing slopes

EXAMPLE #1: Line 1 contains points A(1,5) and B(3,1)Line 2 contains points C(3,3) and D(1,-4)Are the 2 lines parallel? Explain.

Are the two lines parallel?Example #2 Line 1 contains P(0,3) and Q(-2,5) Line 2 contains R(0,-7) and S(3,-10)

Are the lines parallel?

Example #3 Are the lines and

parallel? Explain.

Compare the SLOPES by re-writing in slope-intercept form.

How do you write the equation of a line? There are 3 forms used to write the equation of

a line…

Writing the Equations of Parallel Lines Example #4Write an equation of a line parallel to that contains the point (1,-2).

Identify slope. Use this slope and given point to write equation:

Example #5 Write the equation for the line that is parallel to

y=3x+5 that contains the point (-3,7).

Slope and Perpendicular Lines Perpendicular Lines have slopes that are

opposite, reciprocals of each other. Their slopes’ product is -1. Any vertical and any horizontal line are

perpendicular.

Slope: Perpendicular Slope:

Are the 2 lines perpendicular? To answer this question, do the following:1. Find their slopes. 2. If their slopes are opposite, reciprocal, then

they are perpendicular.

Example #1: Line 1: (-2,3) and (6,-3)Line 2: (-3,-2) and (0,2)

Are the 2 lines perpendicular?2.

3.

4.

Writing the Equation of Perpendicular LinesStep 1. Identify the slope of the given line.

Step 2. Find the slope of the line perpendicular to the given line (opposite, reciprocal)

Step 3. Use the slope from Step 2 and given point to write new equation.

Writing the equation of perpendicular linesExample #5Write the equation of the line that is perpendicular to and passes through the point (1,-2)

Example #6Write the equation for the line that is perpendicular to y=3x+5 that contains the point (-3,7).