Do Now 11/30/11Do Now 11/30/11

Open your textbook to page 318 Open your textbook to page 318 and complete the “If-Then and complete the “If-Then Statement” Activity. With your Statement” Activity. With your partner make one set of “cards.” partner make one set of “cards.” Then answer the questions in Then answer the questions in your notebook.your notebook.

ObjectiveObjective

SWBAT write equations of parallel SWBAT write equations of parallel and perpendicular linesand perpendicular lines. .

If-Then Statements and Their If-Then Statements and Their ConversesConverses

IF-IF-THEN THEN STATEMENTS…STATEMENTS…- - “IF”“IF” stands for a hypothesis stands for a hypothesis- - “THEN”“THEN” stands for a conclusion stands for a conclusion

CONVERSE…CONVERSE…- the converse of a conditional - the converse of a conditional

statement INTERCHANGES the statement INTERCHANGES the hypothesis and conclusion. The converse hypothesis and conclusion. The converse of a true statement is not always of a true statement is not always necessarily true. necessarily true.

If it is a duck, then it has wings.If it is a duck, then it has wings.All ducks have wings.All ducks have wings.

If it is has wings, then it is a duck.If it is has wings, then it is a duck.Airplanes have wings and it is not a duck.Airplanes have wings and it is not a duck.

Section 5.5 “Write Equations of Section 5.5 “Write Equations of Parallel and Perpendicular Parallel and Perpendicular

Lines”Lines”

PARALLEL LINESPARALLEL LINES

– If two nonvertical lines in the same If two nonvertical lines in the same plane have the plane have the same slopesame slope, then , then they are they are parallelparallel..

– If two nonvertical lines in the same If two nonvertical lines in the same plane are plane are parallelparallel, then they have , then they have the the same slope.same slope.

Write an equation of the line that passes through Write an equation of the line that passes through (–3(–3,,–5)–5) and is parallel to the lineand is parallel to the line yy = 3= 3xx – 1.– 1.

STEP 1Identify the slope. The graph of the given equation has a slope of 3. So, the parallel line through (– 3, – 5) has a slope of 3.

STEP 2Find the y-intercept. Use the slope and the given point.

yy = = mxmx + + bb

– – 55 = 3(– 3) + = 3(– 3) + bb4 = 4 = bb

Write slope-intercept formWrite slope-intercept form..

SubstituteSubstitute 33 forfor mm,, - -33 for for xx,, andand - -55 forfor yy..Solve forSolve for bb..

STEP 3

Write an equation. Use y = mx + b.

y = 3x + 4 SubstituteSubstitute 33 forfor mm andand 44 forfor bb..

Write an equation of the line that passes through Write an equation of the line that passes through (–2,11)(–2,11) and is parallel to the lineand is parallel to the line yy = -= -xx + 5 + 5..

STEP 1Identify the slope. The graph of the given equation has a slope of -1. So, the parallel line through (– 2, 11) has a slope of -1.

STEP 2Find the y-intercept. Use the slope and the given point.

yy = = mxmx + + bb

1111 = -1(–2) + = -1(–2) + bb9 = 9 = bb

Write slope-intercept formWrite slope-intercept form..

SubstituteSubstitute -1-1 forfor mm,, - -22 for for xx,, andand 11 11 forfor yy..Solve forSolve for bb..

STEP 3

Write an equation. Use y = mx + b.

y = -x + 9 SubstituteSubstitute -1-1 forfor mm andand 99 forfor bb..

PERPENDICULAR LINESPERPENDICULAR LINES

– If two nonvertical lines in the same If two nonvertical lines in the same plane have slopes that are plane have slopes that are negative negative reciprocalsreciprocals, then the lines are , then the lines are perpendicularperpendicular..

– If two nonvertical lines in the same If two nonvertical lines in the same plane are plane are perpendicularperpendicular, then their , then their slopes are slopes are negative reciprocalsnegative reciprocals

½ and -2 are negative reciprocals.½ and -2 are negative reciprocals.

3 and -1/3 are negative reciprocals.3 and -1/3 are negative reciprocals.

Determine which lines, if any, are parallel or Determine which lines, if any, are parallel or perpendicular.perpendicular.

Line Line aa: : y y = 5= 5x x – 3– 3 Line Line bb:: x x +5+5y y = 2= 2 Line Line cc:: –10–10y y – 2– 2x x = 0= 0

Find the slopes of the linesFind the slopes of the lines..

Write the equations for lines Write the equations for lines a, b, a, b, and and cc in slope-intercept form.in slope-intercept form.

LineLine bb:: x x + 5+ 5y y = 2= 2

55y y = – = – x x + 2+ 2

LineLine cc:: – – 1010y y – 2– 2x x = 0= 0

– – 1010y y = 2= 2xx

y y == –– xx11

55xxy y ==

22

5511

55++

––

LineLine aa:: y y = 5= 5x –x – 3 3

Lines Lines bb and and cc have slopes of have slopes of –1/5, –1/5, so they are so they are parallel. Lineparallel. Line a a has a slope ofhas a slope of 5, 5, the negative the negative reciprocal reciprocal of of –1/5, –1/5, so it is perpendicular to lines so it is perpendicular to lines bb and and cc..

Determine which lines, if any, are parallel or Determine which lines, if any, are parallel or perpendicular.perpendicular.

Line Line aa: : 2x + 6y = -32x + 6y = -3 Line Line bb:: 3x – 8 = y3x – 8 = y Line Line cc:: –1.5y + 4.5x = 6–1.5y + 4.5x = 6

Find the slopes of the linesFind the slopes of the lines..

Write the equations for lines Write the equations for lines a, b, a, b, and and cc in slope-intercept form.in slope-intercept form.

LineLine bb:: 3x – 8 = y3x – 8 = y LineLine cc:: ––1.5y + 4.5x = 1.5y + 4.5x = 66

LineLine aa:: 2x + 6y = -32x + 6y = -3

Lines b and c have slopes of 3, so they are parallel. Line a has a slope of -1/3, the negative reciprocalof 3, so it is perpendicular to lines b and c.

6y = –2x – 3

xy =12

13

––

– 1.5y = -4.5x + 6

y = 3x – 4

Write an equation of the line that passes through (4, – 5) and is perpendicular to the line y = 2x + 3.

STEP 1Identify the slope. The graph of the given equation has a slope of 2. Because the slopes of perpendicular lines are negative reciprocals, the slope of the perpendicular line through (4, –5) is -1/2 .

STEP 2

Find the y-intercept. Use the slope and the given point.

Write slope-intercept form.

– 5 = – (4) + b12

Substitute – for m, 4 for x, and

– 5 for y.

12

y = mx + b

– 3 = b Solve for b.

STEP 3

Write an equation.y = m x + b Write slope-intercept form.

y = – x – 312

Substitute – for m and – 3 for b.1

2

HomeworkHomework

Text p. 322, #8-24 even, 32 & 36Text p. 322, #8-24 even, 32 & 36