Monday, 1/4/10 SWBAT…get ready for the next unit and compute slope Agenda 1. WU (5 min) 2. M&M activity (5 min) 3. Parent functions handout (5 min) 4. Calendar of remaining semester / Announcements (5 min) 5. Complete 16 Q review (15 min) 6. Notes on slope (20 min) Warm-Up: 1. Sit at the table corresponding to your symbol 2. Hole punch your note cards and place… 3. Choose one m&m – do not eat it… yet! HW #1: Slopes of lines (front & back)

Review parent functions handout  Place in toolkit

New unit - what will we be learning Slope Graphing lines  Slope-intercept form  y = mx + b  Point slope form  (y – y 1 ) = m(x = x 1 )  Standard forms  Ax + By = C Writing equations of lines  Slope-intercept form  y = mx + b  Point slope form  (y – y 1 ) = m(x = x 1 )  Standard forms  Ax + By = C Parallel and perpendicular lines Lines of fit

FYI… This is the foundation for upper level math courses such as Geometry, Algebra II, Pre- Calculus, Calculus ACT LOVES THIS STUFF!!!

Monday, 1/4Tuesday, 1/5Wednesday, 1/6Thursday, 1/7Friday, 1/8 SlopeSlope (cont’d) ½ Day: A Writing equations in slope-intercept form (y=mx+b) Graphing linear functions using y=mx+b Monday, 1/11Tuesday, 1/12Wednesday, 1/13Thursday, 1/14Friday, 1/15 Writing equations of lines in slope intercept form (y=mx+b) Writing equations of lines in slope intercept form (cont’d) ½ Day: B Point slope form & Standard form All 3 forms of lines 1. Slope-intercept 2. Point-slope 3. Standard Monday, 1/18Tuesday, 1/19Wednesday, 1/20Thursday, 1/21Friday, 1/22 MLK NO CLASSES Parallel and Perpendicular lines Parallel and Perpendicular lines Lines of best fitLines of best fit/ Final study guide Monday, 1/25Tuesday, 1/26Wednesday, 1/27Thursday, 1/28Friday, 1/29 Study guide ALGEBRA FINAL? END OF Q2 NO CLASSES

Announcements 1. I will be collecting and grading most homeworks 2. To do well on the quizzes, tests, and final, you need to not only be able to use the formulas, but truly understand and apply the concepts 3. You need to complete the “HOTS” problems 4. You can expect: quizzes/week 1. Homework or specific problems from hw 2. WUs 3. Exit slip 2. Lots of practice problems in class 3. Many WU practice problems 4. Many exit slip practice problems 5. Vocabulary note cards are due every Friday

All PPT and HWs are on the Infinity website Math Vocab sheet is on the Infinity website Office Hours: Every Tuesday and Thursday in the Library

For the next 15 minutes… Complete the 16 question “Get ready for the next unit” handout When you finish, cut a piece of graph paper into 8 squares

How do engineers build bridges?

How do engineers build roads?

How do builders build roofs?

How can we write 7% as a fraction?

7% as a fraction?? Remember than any percent is a part of 100.

The grade or incline of a road is the same as slope Here is the picture: 7 feet 100 feet

Slope of a line (m) To find the slope, use the formula 4 4 (elevacion) (desplazamiento)

Slope of a line (m) To find the slope, use the formula 4 4

Slope of a line (m) Find the slope of the following lines: 1 2 A) B) 2 3

Why do we use m for slope? Possibly because m comes from the French word “monter”, which means to climb The earliest textbooks used m, and everyone else just copied it

Slope of a line (m) Is the slope positive or negative? Answer: Positive, read from left to right

Try for yourself Using the graph paper squares, draw lines with the following slopes. Start anywhere on your coordinate plane. A) B) Glue the graphs in your note book

Slope of a line (m) The last 2 lines had a positive slope, let’s look at slopes with negative slopes

Slope of a line (m) We still use rise over run, except the “stairs” are underneath the line. 3 -2

Try for yourself Using the graph paper squares, draw lines with the following slopes. Start anywhere on your coordinate plane. C) D) Glue the graphs in your note book

Your turn

“Official” Definition of Slope Slope is the change in the vertical distance (rise) over the change in the horizontal distance (run) Pendiente: Razon del cambio en la coordenada y (elevacion) al cambio correspondiente en la coordenada x (desplazamiento) a medida que uno se mueve de un punto a otra en una recta.

Find the slope of the line that passes through (1, 0) and (-1, -1). Question (x 1, y 1 ) (x 2, y 2 ) (To see the slope visually… Plot these points. Connect the line (don’t forget arrows)).

1 2 m  What the graph looks like

What is the slope of this line? xy

Horizontal lines have a slope of ___ Vertical lines have a slope of ___ HorizontalVertical m = 0 m = undefined (no slope)

A horizontal lines passes through (2, 5). What other point does the line contain? 1. (2,3) 2. (0,5) 3. (5,10) 4. (0,2)

Practice problem Given Slope 1 = 1/100, Slope 2 = 2/15, Slope 3 = -1/25 Question 1: Which is the steepest? Question 2: Which is the least steep? HW Prob #

Practice Problem Directions: Find the value of r so the line that passes through each pair of point has the given slope. (12, 10), (-2, r), m = -4 HW Prob #12

Tuesday, 1/5/09 SWBAT… compute slope and interpret the meaning of slope (rate of change), given equations, tables, or graphs Agenda 1. WU (10 min) 2. Questions from hw#1 (15 min) 3. Slope as rate of change (15 min) Warm-Up: In the standard (x, y) coordinate plane, what is the slope of the line given by the equation 5x – 4y = 3? HW #1: Slopes of lines collected at end of period

Slope as the rate of change Slope is also known as the rate of change Example: Sam had 5 gallons of gasoline in his bike. After driving 100 miles, he had 3 gallons left.

a.Find the slope of the line b.What does this slope tell us?

Slope as the rate of change a. Find the slope of the line Slope = rise/run = -2/100 = -1/50 b. What does this slope tell us? Since -2/100 = -0.02, we know that Sam’s bike is burning 0.02 gallons of gasoline for every mile that he travels. (The negative value of the slope tells us that the amount of gasoline in the tank is decreasing.)