ObjectiveObjective SWBAT review for Chapter 5 TESTSWBAT review for Chapter 5 TEST. .

Section 5.1 & 5.2 Section 5.1 & 5.2 “Write Equations in “Write Equations in Slope-Intercept Form”Slope-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

slope y-intercept

y-coordinate x-coordinate

Section 5.3 Section 5.3 “Write Linear “Write Linear Equations in Point-Slope Form”Equations in Point-Slope Form”

POINT-SLOPE FORM-POINT-SLOPE FORM-of a linear equation is written as:of a linear equation is written as:

slope

y-coordinatepoint 1

x-coordinatepoint 1

)( 11 xxmyy

y

x

),( 11 yx

),( yx

runrun

riserise

Section 5.4 Section 5.4 “Write Linear “Write Linear Equations in Standard Form”Equations in Standard Form”

The The STANDARD FORMSTANDARD FORM of a of a linear equation is represented aslinear equation is represented as

AAx x ++ BBy y = C= Cwhere A, B, and C are real where A, B, and C are real

numbersnumbers

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

PARALLEL LINESPARALLEL LINES

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

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

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..

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

STEPSTEP 22Find the Find the yy--intercept. Use the slope and the given point.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..

STEPSTEP 33

Write an equation. UseWrite an equation. Use y y = = mx mx + + bb..

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

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

PERPENDICULAR LINESPERPENDICULAR LINES

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

– If two nonvertical lines in the same plane If two nonvertical lines in the same plane are are perpendicularperpendicular, then their slopes are , then their 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..

Section 5.6 “Fit a Line to Data”Section 5.6 “Fit a Line to Data”

a graph used to determine whether there is a graph used to determine whether there is a relationship between paired data.a relationship between paired data.

Scatter PlotScatter Plot

y

x

Scatter plots can show Scatter plots can show trendstrends (patterns) in the data.(patterns) in the data.

y

x

y

x

y

x

Positive correlationPositive correlation Negative correlationNegative correlation Relatively Relatively no correlationno correlation

As As yy tends to increase, tends to increase, xx tends to increase. tends to increase.

As As yy tends to decrease, tends to decrease, xx tends to increase. tends to increase.

xx and and yy have have no apparent no apparent relationship.relationship.

Section 5.7 “Predict with Linear Section 5.7 “Predict with Linear Models”Models”

line that most closely follows line that most closely follows the trend of the data.the trend of the data.

Best-Fitting LineBest-Fitting Line y

x

Linear InterpolationLinear Interpolation

Using a line or its equation to approximate a value BETWEEN two known values.

11

22

33

44

00 11 22 33 44 55 66 77years

heig

ht o

f tr

eeLinear ExtrapolationLinear Extrapolation

Using a line or its equation to approximate a value OUTSIDE the range of known values.

11

22

33

44

00 11 22 33 44 55 66 77years

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ee

Zero of a FunctionZero of a Function

A zero of a function is an x-value for which A zero of a function is an x-value for which f(x) = 0. Because f(x) is the same as y, and y = 0 f(x) = 0. Because f(x) is the same as y, and y = 0 along the x-axis of the coordinate plane, a zero of a along the x-axis of the coordinate plane, a zero of a function is an x-intercept of the function’s graph.function is an x-intercept of the function’s graph.

Find the zero of the function.Find the zero of the function.

f(x) = 3x – 15f(x) = 3x – 15 0 = 3x – 150 = 3x – 15

+15 = +15+15 = +15

15 = 3x15 = 3x3 = 33 = 3

5 = x5 = xThe zero off(x) = 3x -15 is 5.

B-I-N-G-OB-I-N-G-O Complete the Chapter 5 Review on page Complete the Chapter 5 Review on page

345-347 in the text. Complete #1-22 all.345-347 in the text. Complete #1-22 all.

Using your correct answers we will play Using your correct answers we will play BINGO for BONUS points!!!BINGO for BONUS points!!!

23). Write an equation in slope-intercept form that passes through (0,2) and (9,5). 23). Write an equation in slope-intercept form that passes through (0,2) and (9,5).

24). Write an equation in standard form that passes through (-5,-2) and (-4,3). 24). Write an equation in standard form that passes through (-5,-2) and (-4,3).

23). y = 1/3x + 2 23). y = 1/3x + 2

24). –x + y = 7 24). –x + y = 7

BingoBingo 1) negative1) negative 2) extrapolation2) extrapolation 3) x-intercept3) x-intercept 4) y = 3x – 10 4) y = 3x – 10 5) y = 4/9x + 55) y = 4/9x + 5 6) y = -2/11x + 76) y = -2/11x + 7 7) y = -1.25x + 25; $22.507) y = -1.25x + 25; $22.50 8) y = 4x + 118) y = 4x + 11 9) y = x + 39) y = x + 3 10) y = -3x + 2010) y = -3x + 20 11) y – 7 = -6(x – 4)11) y – 7 = -6(x – 4) 12) y + 2 = -1/3(x + 3)12) y + 2 = -1/3(x + 3)

13) y + 2 = -6/11(x – 8)13) y + 2 = -6/11(x – 8) 14) y – 100 = -7/10(x – 25); 14) y – 100 = -7/10(x – 25);

54.5 miles 54.5 miles 15) 4x + y = -115) 4x + y = -1 16) -3x + y = -216) -3x + y = -2 17) 0.07x + 0.04y =5; 17) 0.07x + 0.04y =5; 18) (a) y = -4x + 2; 18) (a) y = -4x + 2; (b) y = 1/4x + 2(b) y = 1/4x + 2 19) (a) y = -2x + 1; 19) (a) y = -2x + 1; (b) y = 1/2x – 4 (b) y = 1/2x – 4 20) (a) y = 3/4x – 4½; 20) (a) y = 3/4x – 4½; (b) y = -4/3x + 8(b) y = -4/3x + 8 21) positive correlation21) positive correlation 22) about 5.75 hours22) about 5.75 hours