Mindjog 9/1 Given the points (-1, 4) and (2, 8), find: Given the points (-1, 4) and (2, 8), find: The distance, slope and midpoint The distance, slope and midpoint The equation of the line passing through the 2 points The equation of the line passing through the 2 points

OBJECTIVE SWBAT SWBAT explore and exhaust all knowledge of linear functions explore and exhaust all knowledge of linear functions

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

Convert the Equation Find the slope and y-intercept, then sketch. Find the slope and y-intercept, then sketch. 3y – 5x = 15 (standard) 3y – 5x = 15 (standard) -2x – 6y + 15 = 0 (general) -2x – 6y + 15 = 0 (general)

Slope Describe a Describe a Positive slope Positive slope Negative slope Negative slope Zero slope Zero slope Undefined slope Undefined slope

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

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

Other Linear Topics Explain x = -2, and y = 4. Explain x = -2, and y = 4. Parallel lines? Parallel lines? Perpendicular lines? Perpendicular lines?

ADMINISTRATIVE STUFF Syllabus Syllabus Parent Survey Parent Survey

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

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

OBJECTIVE (9/2 and 9/3) SWBAT SWBAT Use applications and models of linear equations (in groups on 9/2) Use applications and models of linear equations (in groups on 9/2)

LINEAR EQUATION Definition? Definition? Variable to the first degree! Variable to the first degree!

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

SOLUTION 4(x + 3) = x 4(x + 3) = x x = 14 x = 14

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

SOLUTION.15x+.3(3)=.2(3 + x).15x+.3(3)=.2(3 + x) x = 6 x = 6

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

SOLUTION 2.5(x+5) = 2x (x+5) = 2x + 40 x = 55 x = 55

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

SOLUTION.0465(.5x) (410,000 – x) = 14, (.5x) (410,000 – x) = 14,961 x = 200,000 x = 200,000

CLASSWORK (9/3) Ditto 1.2 Applications and Modeling… Ditto 1.2 Applications and Modeling… Stand if You Agree Stand if You Agree

ADMIN (9/2) Syllabus/Student Survey Syllabus/Student Survey Parent Survey Parent Survey

HOMEWORK (9/2) Textbook, p. 89 #’s even Textbook, p. 89 #’s even p #’s 2-40 even p #’s 2-40 even

HOMEWORK (9/3) Finish Ditto 1.2 Applications and Modeling… Finish Ditto 1.2 Applications and Modeling…

Mindjog 9/4 Suppose that tuition is $69.69 per credit hour and that student fees are fixed at $25. Antonio paid $1, for his fall classes. How many credit hours did he sign up for?

CLASSWORK Pair Get to know you