On a quiz show, 30 points are given for correct On a quiz show, 30 points are given for correct answers to Regular questions, and 60 points are answers to Regular questions, and 60 points are given for correct answers in the Bonus round. Let given for correct answers in the Bonus round. Let RR represent the number of regular questions represent the number of regular questions answered correctly and answered correctly and BB represent the number represent the number of bonus questions answered correctly.of bonus questions answered correctly.

a)a) Write an Write an expressionexpression that give the total number of points that give the total number of points earned. earned.

b) b) Suppose a contestant earned 900 points. Write an Suppose a contestant earned 900 points. Write an equationequation relating relating RR, , BB, and the number of points earned. , and the number of points earned.

c)c) If the contestant answered 20 regular questions correctly If the contestant answered 20 regular questions correctly and earned 900 points, how many and earned 900 points, how many bonusbonus questions were questions were answered correctly?answered correctly?

d)d) Find another possible solution to the equation in b.Find another possible solution to the equation in b.

30R + 60B30R + 60B

30R + 60B = 90030R + 60B = 900

55 Bonus Questions Bonus Questions

3-43-4The Graph ofThe Graph ofAx + By = CAx + By = C

Standard FormStandard FormAx + By = CAx + By = C

• • A has to be A has to be POSITIVEPOSITIVE!!!!!!• • A and B can not be A and B can not be FRACTIONSFRACTIONS or or DECIMALSDECIMALS!!!!!!•• A and B can not A and B can not BOTHBOTH be zero. be zero.

•• The graph of Ax + By = C, where A and B are The graph of Ax + By = C, where A and B are not bothnot both 0, is a 0, is a lineline..

Finding Useful InformationFinding Useful Information

-To find the x-intercept:-To find the x-intercept:•• Substitute 0 in for y.Substitute 0 in for y.•• Solve for xSolve for x•• x = C / Ax = C / A

-To find the y-intercept:-To find the y-intercept:•• Substitute 0 in for x.Substitute 0 in for x.•• Solve for ySolve for y•• y = C / By = C / B

-To find slope:-To find slope:•• Subtract AxSubtract Ax•• Divide by BDivide by B•• m = -A / Bm = -A / B

Standard Form : Ax + By = C

ExampleExample 05/05/2305/05/23

Give an equation in Standard Formfor the line with y-int of – 5 and slope . Identify the x-int.

43

543

xy

CByAx

543

yx

)543(4 yx

2043 yx

320int x

5int y

←Standard Form→

05/05/2305/05/23ExampleExample 05/05/2305/05/23

Give an equation in Standard Formfor the line with y-int of 7 and slope . Identify the x-int.

51

751

xy

CByAx

751

yx

)751(5 yx

355 yx35int x7int y

←Standard Form→

05/05/2305/05/23

Complete the TableStandard FormStandard FormAx + By = CAx + By = C

SlopeSlope y-intercepty-intercept x-interceptx-intercept

5x – 10y = 305x – 10y = 30

––2/52/5 4 4

6x – 7y = –426x – 7y = –42

nonenone – – 99

1/21/2 – – 33 66

2x + 5y = 202x + 5y = 20 1010

6/76/7 66 – – 77

x = – 9 x = – 9 undefinedundefined

Graphing by InterceptsGraphing by InterceptsTo Graph by InterceptsTo Graph by Intercepts• Find x-interceptFind x-intercept• Plot on GraphPlot on Graph• Find y-interceptFind y-intercept• Plot on GraphPlot on Graph• Draw line through the Draw line through the

pointspoints

4x + 3y = 124x + 3y = 124x + 3(0) =124x + 3(0) =12 x-int = 3x-int = 3

4x + 3y = 124x + 3y = 124(0) + 3y = 124(0) + 3y = 12 y-int = 4y-int = 4

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Graphing by InterceptsGraphing by InterceptsGraph the equation: Graph the equation:

6x – 4y = 246x – 4y = 24using its intercepts.using its intercepts.x-int = ?x-int = ?

y – int = ?y – int = ?

6x – 4(0) =246x – 4(0) =24

6(0) – 4y =246(0) – 4y =24

x-int = 4(4, 0)

y-int = –6(0, –6)

AssignmentAssignment• Lesson Master 3-4Lesson Master 3-4• Pages 160-161 #’s 6, 8, 9,12-18, 20-22.Pages 160-161 #’s 6, 8, 9,12-18, 20-22.

• Study for Quiz on Sections 3-1 to 3-3!!!!!Study for Quiz on Sections 3-1 to 3-3!!!!!