HomeworkHomeworkText p. 407, #8-10, 12-30 evensText p. 407, #8-10, 12-30 evens

8) positive; 3/48) positive; 3/4 9) negative; -3/49) negative; -3/4 10) undefined10) undefined 12) (0,-1) & (2, -1); m = 012) (0,-1) & (2, -1); m = 0 14) (6,0) & (0,3); m = -1/214) (6,0) & (0,3); m = -1/2 16) (3,0) & (3,5); m = undefined16) (3,0) & (3,5); m = undefined 18) 18)

20) 20)

22) 222) 2 24) undefined24) undefined 26) 7/826) 7/8 28) -528) -5 30) undefined30) undefined

Copy HW in your planner.Text p. 415, #10-12, 14-18 evensQuiz sections 8.3-8.5 Friday

NJASK

Deborah and Cormac are building a sandcastle. They plan to construct a rectangular pyramid with dimensions 5 feet wide by 5 feet long by 3 feet high. To transport this volume of sand, they use a cylindrical can with a diameter of 1 foot and an height of 9 inches. About how many cans of sand do they need to create this pyramid?

Do Now 4/3/13Do Now 4/3/13

In your notebook, identify In your notebook, identify the slope of each colored line. the slope of each colored line. The black lines are the The black lines are the x-and y-axis. x-and y-axis.

Positive slope

Negative slope

Slope of 0

Undefined

ObjectiveObjective

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

Section 8.4 “Section 8.4 “The Slope of a LineThe Slope of a Line””

SLOPE-SLOPE-the ratio of the vertical change (the rise) to the ratio of the vertical change (the rise) to the horizontal change (the run) between the horizontal change (the run) between any two points on a line.any two points on a line.

Slope = rise = change in y run change in x

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 8.5 “Section 8.5 “Graph Using Slope-Graph Using Slope-Intercept FormIntercept Form””

SLOPE-INTERCEPT FORM-SLOPE-INTERCEPT FORM-

a linear equation written in the forma linear equation written in the form

y = mx + by = mx + b

slopeslope y-intercepty-intercept

y-coordinatey-coordinate x-coordinatex-coordinate

Identifying Slope and the Y-InterceptIdentifying Slope and the Y-Intercept

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?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 FormGraph an Equation Using the Slope-Intercept Form

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 FormGraph an Equation Using the Slope-Intercept Form

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-InterceptGraph Using Slope and the Y-Intercept

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-InterceptGraph Using Slope and the Y-Intercept

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

Write an equation for the line. Write an equation for the line.

y = x – 1 y = x – 1

slopeslope y-intercepty-intercept

Slope ofSlope of 1/1 1/1

means: means: run

rise

1

1

y-intercept = -1y-intercept = -1

Slope = 1/1Slope = 1/1

y = mx + b y = mx + b

Parallel LinesParallel Linestwo lines in the same plane are parallel if two lines in the same plane are parallel if

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

y = y = 33x + 2x + 2

y = y = 33x – 4 x – 4

Perpendicular LinesPerpendicular Linestwo lines in the same plane are perpendicular if two lines in the same plane are perpendicular if

they intersect at right angles. Because slope gives they intersect at right angles. Because slope gives the rate at which a line rises or falls, two lines with the rate at which a line rises or falls, two lines with slopes that are slopes that are NEGATIVE RECIPROCALSNEGATIVE RECIPROCALS are are PERPENDICULARPERPENDICULAR..

y = y = -2-2x + 2x + 2

y = y = 1/21/2x – 4 x – 4

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

4/3 and -3/4 4/3 and -3/4 are negative reciprocals.are negative reciprocals.

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..

HomeworkHomework Text p. 415, #10-12, 14-18 evensText p. 415, #10-12, 14-18 evens