Slopes and Equations of Lines Rigor: Use slope to partition a segment; write equation of lines perpendicular and parallel to another line Relevance – These.

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Presentation transcript:

Slopes and Equations of Lines Rigor: Use slope to partition a segment; write equation of lines perpendicular and parallel to another line Relevance – These sections will get you ready for coordinate geometry!

3-5 Notes: What is slope? zeronegative positive undefined

EX 1: Calculate the slope of each line a) b) of the line going through (4, 7) and (9, 2).

What do you notice about the slopes? Parallel lines Perpendicular lines

Slope of Parallel & Perpendicular Lines If 2 lines are parallel, the slopes will be the same (when simplified). If 2 lines are ┴, the slopes will be opposite reciprocals. ( )

Ex 3: Interpreting slope as rate of change Tony is driving from Dallas, TX to Atlanta, GA. At 3pm he is 180 miles from Dallas. At 5:30pm, he is 330 miles from Dallas. Calculate and interpret the slope of the line comparing Tony’s distance from Dallas and his travel time.

Partitioning a segment Partitioning a segment divides the segment into parts based on a ratio. Step 1: draw slope triangle and label rise and run. Step 2: write the first ratio number as a fraction or percent over the total parts (add ratio numbers) Step 3: multiply percent by rise and multiply percent by run Step 4: add the product to the first coordinates to get the partition coordinates

3-5 Classwork Textbook pg 186 #14 – 17, 19, 20, 25 Core book pg 114 #1, 3, Homework Core book pg 115 # 1 – 8 HW Due Thursday for periods 1, 3, 5 HW Due Friday for periods 2, 4, 7

3-6 Notes: turn to core book pg 117 Highlight slope-intercept form and point-slope form of a line Write standard form, vertical line, and horizontal line formulas Standard Form: Ax + By = C (A, B, & C are integers, A is +) Vertical Line: x = a Horizontal line: y = b

Ex 1: Write the equation of each line in the given form a) 5x + 2y = 16 in slope – intercept form b) The line with a slope of 9 that passes through (4, - 3) in slope – intercept form c) The line through (0, 4) and (-1, 2) in point – slope form

Ex 2: Graph each line y + 3 = -2(x – 1) x = - 2

Core Book Examples Fill in examples 1 and 2 on pages 117 – 118

3-6 Classwork from the Core book Page 119 #1 – 10 Page 120 #12 – Homework from the core book Page 121 #1 – 9 Due Thursday for periods 1, 3, & 5 Due Friday for periods 2, 4, & 7