CONCEPT: W R I T I N G E Q U AT I O N S O F L I N E SEQ: H O W D O W E W R I T E T H E E Q U AT I O N O F A L I N E T H AT I S PA RA L L E L O R P E R P E N D I C U L A R T O A G I V E N L I N E ? ( G . G P E . 5 )VOCABULARY : S LO P E , PA RA L L E L , P E R P E N D I C U L A R , R E C I P R O C A L

LESSON 6.1BWRITING EQUATIONS OF PARALLEL

AND PERPENDICULAR LINES

FIRST WORD

•Create an acrostic about everything you remember from the previous lesson using the word. • SLOPE

INTRODUCTION

• Parallel lines are lines which never touch or intersect.• Perpendicular lines are lines which meet

or intersect and create a 90° angle aka a right angle. • We can find the equation of two lines

which are parallel or perpendicular and prove whether the lines are parallel or perpendicular.

PARALLEL LINES

•Lines which are parallel always have the same slope or value for m, but a different y-intercept or value for b.• Ex. are parallel lines because they have the same slope but different y-intercepts.

EXAMPLE 1

• Two lines, are linear equation. Line has the equation . Line has the equation . Are they parallel?

EXAMPLE 2

• The two lines in the graph to the right, are shown. Are they parallel?

YOU TRY 1

• You are the given two equations of two different lines, Are these lines parallel?

YOU TRY 2

• Are these lines parallel? Explain

EXAMPLE 3

• A line which contains the point (2,5) is parallel to the line . Find the equation to this line.

1. State the point-slope formula. 2. Identify m,

3. Substitute the values into the formula.

4. Simplify into slope-intercept form.

EXAMPLE 4

• Using the graph to the right, find the equation of a parallel line which passes through the point which is not on the given line.

1. Find the slope of the given line. 2. Identify m,

3. Substitute the values into the point-slope formula.

4. Simplify into slope-intercept form.

YOU TRY 3

• A line which contains the point (0,-11) is parallel to the line . Find the equation to this line.

1. State the point-slope formula. 2. Identify m,

3. Substitute the values into the formula.

4. Simplify into slope-intercept form.

PERPENDICULAR LINES

• Lines are always perpendicular if their slopes are a negative reciprocal of one another. Perpendicular lines can have the same y-intercepts though.• Ex. are perpendicular lines with the same y-intercepts.

Another example would be . These two lines are perpendicular because of their slopes but have different y-intercepts.

EXAMPLE 5

• Two lines are given,. Are they perpendicular?

EXAMPLE 6

• The two lines in the graph to the right, are shown. We need to determine if the two lines are perpendicular.

YOU TRY 4

• You are given two equations, Are these two lines perpendicular?

YOU TRY 5

• Are these lines perpendicular? Explain

EXAMPLE 7

• A line which contains the point (2,5) is perpendicular to the line . Find the equation to this line.

1. State the point-slope formula. 2. Identify m, Find the negative reciprocal of m.

3. Substitute the values into the formula. Use the new slope you found for m.

4. Simplify into slope-intercept form.

EXAMPLE 8

• Using the graph to the right, find the equation of a parallel line which passes through the point which is not on the given line.

1. Find the slope of the given line. 2. Identify m, Find the negative reciprocal of m.

3. Substitute the values into the point-slope formula. Use the new slope you found for m.

4. Simplify into slope-intercept form.

YOU TRY 6

• A line which contains the point (0,5) is perpendicular to the line . Find the equation to this line.

1. State the point-slope formula. 2. Identify m, Find the negative reciprocal of m.

3. Substitute the values into the formula. Use the new slope you found for m.

4. Simplify into slope-intercept form.

3-2-1

• List three important facts you learned about today.• List two concepts you already knew.• List one task you still need to work on.