do now 11/2/09
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Do Now 11/2/09. Take out HW from Friday. Practice worksheet 4.4 form C evens Copy HW in your planner. Text p.247 #4-38 even Be ready for slope quiz. 2) undefined 4) zero 6) positive 8) -11/6 10) 4/3 12) 0 14) -2/3 16) 3/5 18) undefined 20) 4/7 22) 0. 24) 1/6 26) -7 28) -1 - PowerPoint PPT PresentationTRANSCRIPT
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