Mindjog 9/1Mindjog 9/1 Given the points (-1, Given the points (-1, 4) and (2, 8), find:4) and (2, 8), find:

The distance, slope The distance, slope and midpointand midpoint

The equation of the The equation of the line passing through line passing through the 2 pointsthe 2 points

OBJECTIVEOBJECTIVESWBAT SWBAT

explore and explore and exhaust all exhaust all knowledge of knowledge of linear functionslinear functions

Linear FunctionsLinear Functions

Sketch the Sketch the function f(x) = -function f(x) = -(3/4)x + 7(3/4)x + 7

Convert the EquationConvert the EquationFind the slope and Find the slope and y-intercept, then y-intercept, then sketch.sketch.

3y – 5x = 15 3y – 5x = 15 (standard)(standard)

-2x – 6y + 15 = 0 -2x – 6y + 15 = 0 (general)(general)

SlopeSlopeDescribe a Describe a

Positive slopePositive slopeNegative slopeNegative slopeZero slopeZero slopeUndefined slopeUndefined slope

What if…What if…The line through The line through the points (-2, the points (-2, 6) and (4, y) has 6) and (4, y) has a slope of 3. a slope of 3. Find y.Find y.

Linear EquationsLinear EquationsGiven point (-6,4) Given point (-6,4) and slope 1/2, and slope 1/2, write the equation write the equation of the line in slope of the line in slope intercept and intercept and general form.general form.

Other Linear TopicsOther Linear Topics

Explain x = -2, Explain x = -2, and y = 4.and y = 4.

Parallel lines?Parallel lines?Perpendicular Perpendicular lines?lines?

ADMINISTRATIVE STUFFADMINISTRATIVE STUFF

SyllabusSyllabusParent SurveyParent Survey

Mindjog 9/2Mindjog 9/2Write the equation Write the equation of the line of the line perpendicular to 3x perpendicular to 3x + 7y = 21 but + 7y = 21 but passing through the passing through the origin. Sketch both.origin. Sketch both.

MINDJOG 9/3MINDJOG 9/3A chemist needs a 20% A chemist needs a 20% solution of alcohol. She has solution of alcohol. She has a 15% solution on hand, as a 15% solution on hand, as well as a 30% solution. How well as a 30% solution. How many liters of the 15% many liters of the 15% solution should she add to solution should she add to 3L of the 30% solution to 3L of the 30% solution to obtain her 20% solution?obtain her 20% solution?

OBJECTIVE (9/2 and 9/3)OBJECTIVE (9/2 and 9/3)

SWBATSWBATUse applications Use applications and models of and models of linear equations linear equations (in groups on 9/2)(in groups on 9/2)

LINEAR EQUATIONLINEAR EQUATION

Definition?Definition?

Variable to the first degree!Variable to the first degree!

Applications of Linear FunctionsApplications of Linear Functions If the length of each side of If the length of each side of a square is increased by a square is increased by 3cm, the perimeter of the 3cm, the perimeter of the new square is 40cm more new square is 40cm more than twice the length of than twice the length of each side of the original each side of the original square. Find the square. Find the dimensions of the original dimensions of the original square.square.

SOLUTIONSOLUTION

4(x + 3) = 40 + 4(x + 3) = 40 + 2x2x

x = 14x = 14

Applications of Linear FunctionsApplications of Linear FunctionsA chemist needs a 20% A chemist needs a 20% solution of alcohol. She has solution of alcohol. She has a 15% solution on hand, as a 15% solution on hand, as well as a 30% solution. How well as a 30% solution. How many liters of the 15% many liters of the 15% solution should she add to solution should she add to 3L of the 30% solution to 3L of the 30% solution to obtain her 20% solution?obtain her 20% solution?

SOLUTIONSOLUTION

.15x+.3(3)=.2(3 + .15x+.3(3)=.2(3 + x)x)

x = 6x = 6

Applications of Linear FunctionsApplications of Linear FunctionsMaria and Jake are Maria and Jake are traveling to a business traveling to a business conference. The trip takes conference. The trip takes 2hrs for Maria and 2.5hrs 2hrs for Maria and 2.5hrs for Jake, since he lives for Jake, since he lives 40mi farther away. Jake 40mi farther away. Jake travels 5mph faster than travels 5mph faster than Maria. Find their average Maria. Find their average rates.rates.

SOLUTIONSOLUTION

2.5(x+5) = 2x + 2.5(x+5) = 2x + 4040

x = 55x = 55

Applications of Linear FunctionsApplications of Linear Functions An artist has sold a painting for An artist has sold a painting for

$410,000. He needs some of the $410,000. He needs some of the money in 6 months and the rest money in 6 months and the rest in 1yr. He can get a treasury in 1yr. He can get a treasury bond for 6 months at 4.65% and bond for 6 months at 4.65% and one for a year at 4.91%. His one for a year at 4.91%. His broker tells him the two broker tells him the two investments will earn a total of investments will earn a total of $14,961. How much should be $14,961. How much should be invested at each rate?invested at each rate?

SOLUTIONSOLUTION

.0465(.5x) .0465(.5x) + .0491(410,000 + .0491(410,000 – x) = 14,961– x) = 14,961

x = 200,000x = 200,000

CLASSWORK (9/3)CLASSWORK (9/3)

Ditto 1.2 Ditto 1.2 Applications and Applications and Modeling…Modeling…

Stand if You Stand if You AgreeAgree

ADMIN (9/2)ADMIN (9/2)

Syllabus/Student Syllabus/Student SurveySurvey

Parent SurveyParent Survey

HOMEWORK (9/2)HOMEWORK (9/2)Textbook, p. 89 Textbook, p. 89 #’s 50-60 even#’s 50-60 even

p. 97-100 #’s 2-p. 97-100 #’s 2-40 even 40 even

HOMEWORK (9/3)HOMEWORK (9/3)

Finish Ditto 1.2 Finish Ditto 1.2 Applications and Applications and Modeling…Modeling…

Mindjog 9/4Mindjog 9/4

Suppose that tuition is Suppose that tuition is $69.69 per credit $69.69 per credit hour and that student hour and that student fees are fixed at $25. fees are fixed at $25. Antonio paid Antonio paid $1,070.35 for his fall $1,070.35 for his fall classes. How many classes. How many credit hours did he credit hours did he sign up for?sign up for?

CLASSWORKCLASSWORK

Pair Get to know Pair Get to know youyou