Do Now 11/2/09Do Now 11/2/09

Take out HW from Friday.Take out HW from Friday.Practice worksheet 4.4 form C evensPractice worksheet 4.4 form C evens

Copy HW in your planner.Copy HW in your planner.Text p.247 #4-38 evenText p.247 #4-38 even

Be ready for slope quiz.Be ready for slope quiz.

Homework Homework Practice worksheet 4.4 Form CPractice worksheet 4.4 Form C 2) undefined2) undefined 4) zero4) zero 6) positive 6) positive 8) -11/68) -11/6 10) 4/310) 4/3 12) 012) 0 14) -2/314) -2/3 16) 3/516) 3/5 18) undefined18) undefined 20) 4/720) 4/7 22) 022) 0

24) 1/624) 1/6 26) -726) -7 28) -128) -1 30) -430) -4 32) a) From 1996 32) a) From 1996

to 1998. b) From to 1998. b) From 1996 to 1998. c) 1996 to 1998. c) Overall, the slope Overall, the slope of both lines is of both lines is positive meaning positive meaning that fuel that fuel consumption has consumption has increased over the increased over the 10 year period.10 year period.

ObjectiveObjective

SWBAT graph linear equations SWBAT graph linear equations using slope-intercept form using slope-intercept form

Slope ReviewSlope Review

The slope The slope m m of a line passing through two pointsof a line passing through two points

and is the ratio of the rise and is the ratio of the rise change to the run. change to the run.

),( 11 yx ),( 22 yx

m

y

x

),( 11 yx

),( 22 yx

runrun

riserise)( 12 yy

)( 12 xx

Section 4.5 “Section 4.5 “Graph Using Graph Using Slope-Intercept FormSlope-Intercept Form””

SLOPE-INTERCEPT FORM-SLOPE-INTERCEPT FORM-a linear equation written in the a linear equation written in the formform

y = mx + by = mx + b

slopeslope y-intercepty-intercept

y-coordinatey-coordinate x-coordinatex-coordinate

Identifying Slope and the Y-Identifying Slope and the Y-InterceptIntercept

run

rise

1

3

y =y = 3 3x +x + 4 4

33x +x + y =y = 2 2

The equation is in the formThe equation is in the form yy == m x +m x + b.b.SoSo,, the slope the slopeof the line is of the line is 33,, and the and the y-y-intercept isintercept is 4.4.

Rewrite the equation in slope-intercept form by Rewrite the equation in slope-intercept form by solving for solving for yy..

y = mx + by = mx + b

y =y = -3x + 2 -3x + 2y =y = 2 – 3x 2 – 3x

The line has a slope of The line has a slope of – 3– 3 and a and a y y--intercept of intercept of 2.2.

Is this in slope-intercept form?

Slope of 3 means: Slope of 3 means:

run

rise

1

3

Identify the slope and Identify the slope and yy--intercept of the line with the intercept of the line with the given equation.given equation.

33x x – 3– 3y =y = 12 12

ANSWERANSWER

The line has a slope of The line has a slope of 11 and a and a y y--intercept of intercept of –4–4..

Rewrite the equation in slope-intercept form by solving for Rewrite the equation in slope-intercept form by solving for yy..

Divide Divide 33 by equation. by equation.

33x x –– 1212 == 33yy Rewrite original equation.Rewrite original equation.

yy 33x – x – 1212==33

yy x x – 4– 4== Simplify.Simplify.

11

22

33

44

55

00 11 22 33 44 55 66

y-axisy-axis

x-axisx-axis-6-6 -5-5 -4-4 -3-3 -2-2 -1-1

-5-5

-4-4

-3-3

-2-2

-1-1

Graph an Equation Using the Slope-Intercept Graph an Equation Using the Slope-Intercept FormForm

Graph the equation Graph the equation y = 2 - 2xy = 2 - 2x..

xy 22 Rewrite in slope-intercept formRewrite in slope-intercept form

22 xy

slopeslope y-intercepty-intercept

Slope ofSlope of -2 means: -2 means: run

rise

1

2

Slope ofSlope of -2 means: -2 means: run

rise

1

2OROR

11

22

33

44

55

00 11 22 33 44 55 66

y-axisy-axis

x-axisx-axis-6-6 -5-5 -4-4 -3-3 -2-2 -1-1

-5-5

-4-4

-3-3

-2-2

-1-1

Graph an Equation Using the Slope-Intercept Graph an Equation Using the Slope-Intercept FormForm

Graph the equation Graph the equation y = -3 + 2/3xy = -3 + 2/3x..

xy3

23

Rewrite in slope-intercept formRewrite in slope-intercept form

33

2 xy

slopeslope y-intercepty-intercept

Slope ofSlope of 2/3 2/3

means: means: run

rise

3

2

Slope ofSlope of 2/3 2/3

means: means: run

rise

3

2OROR

Graph Using Slope and the Y-Graph Using Slope and the Y-InterceptIntercept

Graph the equationGraph the equation 22x +x + y =y = 3. 3.

STEPSTEP 11Rewrite the equation in slope-intercept form.Rewrite the equation in slope-intercept form.yy –– 22x +x + 3 3==

Identify the slope and the Identify the slope and the yy--intercept.intercept.STEPSTEP 22

STEPSTEP 33

Plot the point that corresponds to the Plot the point that corresponds to the y-y-intercept,intercept,(0, 3).(0, 3).

STEPSTEP 44

Use the slope to locate a second point on the line. Draw a line Use the slope to locate a second point on the line. Draw a line through the two points.through the two points.

= –= – 2 2mm andand = = 33bb

Slope of -2 means: Slope of -2 means:

run

rise

1

)2(

Graph Using Slope and the Y-Graph Using Slope and the Y-InterceptIntercept

Graph the equationGraph the equation 3y – 2x =3y – 2x = 3. 3.

STEPSTEP 11Rewrite the equation in slope-intercept form.Rewrite the equation in slope-intercept form.

Identify the slope and the Identify the slope and the yy--intercept.intercept.STEPSTEP 22

STEPSTEP 33

Plot the point that corresponds to the Plot the point that corresponds to the y-y-intercept,intercept,(0, 1).(0, 1).

STEPSTEP 44

Use the slope to locate a second point on the line. Draw a line Use the slope to locate a second point on the line. Draw a line through the two points.through the two points.

= = 2/32/3mm andand = 1= 1bb

y = + y = + 112233

xx

Slope of 2/3 means: Slope of 2/3 means:

run

rise

3

2

Parallel Parallel LinesLinestwo lines in the same plane are two lines in the same plane are

parallel if they never intersect. parallel if they never intersect. Because slope gives the rate at Because slope gives the rate at which a line rises or falls, two lines which a line rises or falls, two lines with the SAME SLOPE are PARALLEL.with the SAME SLOPE are PARALLEL.

Determine which of the lines are parallelDetermine which of the lines are parallel..

Find the slope Find the slope of each lineof each line.. Line Line aa:: mm == – – 11 – – 00

– – 11 – – 22

– – 33 – – ((––11 ))00 – – 55

==–– 11–– 33

1133==

Line Line b:b: m m == –– 22–– 55== 22

55==

Line Line c:c: m m == – – 55 – – ((––3)3) – – 2 – 2 – 44

–– 22–– 66==

11 33==

Line Line aa and line and line cc have the same slope, so they are parallelhave the same slope, so they are parallel..

HomeworkHomeworkText p.247 #4-38 evenText p.247 #4-38 even

2424

HomeworkHomeworkPractice Form C evensPractice Form C evens

2) slope = -6; y-int = 192) slope = -6; y-int = 19 4) slope = -3/2; y-int = 44) slope = -3/2; y-int = 4 6) slope = 4/3; y-int = 36) slope = 4/3; y-int = 3 8) slope = 4/9; y-int = -28) slope = 4/9; y-int = -2 10 – 18) on overhead10 – 18) on overhead 20) line through (-1,3) and (0,-3) and line through 20) line through (-1,3) and (0,-3) and line through

(0,2) and (1,-4) both have slopes of -6(0,2) and (1,-4) both have slopes of -6 22) parallel; slopes of 0.522) parallel; slopes of 0.5 24) -3824) -38 26) -226) -2 28) $6; the cost increases by $2 per hour28) $6; the cost increases by $2 per hour

Practice Form BPractice Form B#2-22 even#2-22 even

2) slope -4; y-int 102) slope -4; y-int 10 4) slope -4; y-int 34) slope -4; y-int 3 6) slope -2/5; y-int 26) slope -2/5; y-int 2 8) slope -3/2; y-int ½8) slope -3/2; y-int ½ 10) slope -1; y-int 3/510) slope -1; y-int 3/5 12) slope undefined; 12) slope undefined;

y-int noney-int none 14) B14) B

16) overhead16) overhead 18) overhead18) overhead 20) overhead20) overhead 22) line through (-1,-4) 22) line through (-1,-4)

and (0,2) and line and (0,2) and line through (1,3) and (2,9)through (1,3) and (2,9)

24) no24) no 26) no26) no 28) yes28) yes 30) a&b) overhead c) 30) a&b) overhead c)

$12$12