Sections 3-5 and 3-6 Slopes, Partitions, 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!

Partitioning a segment graphically Ex 1: Find the coordinates of point P that partitions the directed segment from C(-3, 2) and D( 5, 6) into a ratio of 3 to 1. Partitioning a segment divides the segment into parts based on a ratio. Step 1: draw slope triangle and count the rise and run. DO NOT simplify slope! Step 2: add the 2 numbers in the ratio to get the total number of parts; draw vertical or horizontal segments that divide the rise or run into that many equal parts Step 3: plot the point on the segment so the correct number of parts are on each side.

Partitioning a segment Ex 2: Find the coordinates of point P that partitions the directed segment from C(3, 1) and D( 6, 7) into a ratio of 2 to 1.

Working Backwards to Partition a Segment Ex 3: 𝐻𝐾 is divided by point J at a ratio of 3:2. If H(-6, -1) and J(0, 2), what are the coordinates of point K?

Partitioning Segments Algebraically When partitioning a segment, the coordinates don’t always have to be integers! Turn in your workbook to page 113 for an example. Honors classes – also do workbook pg 114 #3

What is slope? Slope is the rate of vertical change divided by the horizontal change Formula: m =rise/run or 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 4 types of slopes positive undefined zero negative

EX 4: 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 and the y-intercepts will be different (when simplified). If 2 lines are ┴, the slopes will be opposite reciprocals. ( ) If 2 lines have the same slope AND same y-intercept they coincide.

EX 6: Are the lines parallel, ⊥, or neither? A) 𝑆𝑇 has S(-2, 2) & T(5, -1) B) C) 𝐴𝐵 has A(2,1) & B(1, 5) 𝑈𝑉 has U(3, 4) & V(-1, -4) 𝐶𝐷 has C(4, 2) & D(5, -2)

Ex 7: Interpreting slope as rate of change Tony is driving on a highway 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.

3-5 Assignments Primary Assignment: join.quizizz.com Codes: Period 1: 426952 (due Monday) Period 5: 467070 (due Monday) Period 6: 749259 (due Tuesday) Secondary Assignment: Workbook pg 115 ALL and Textbook pg 185 #6-9

3-5 Assignments Primary Assignment: join.quizizz.com Codes: Period 2: (due Tuesday) Period 4: (due Tuesday) Period 7: (due Tuesday) Secondary Assignment: Workbook pg 115 #1-6 and Textbook pg 185 #6-9

3-6 Notes: turn to workbook 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 5x + 2y = 16 in slope – intercept form The line with a slope of 9 that passes through (4, - 3) in slope – intercept form The line through (0, 4) and (-1, 2) in point – slope form

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

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

3-6 Workbook Assignments (Honors) Primary Assignment: pg 119 #1 – 9 odds, pg120 #12 – 18 evens, 19, pg121 #1, 5 – 9 Due Thursday 11/2 for periods 1 & 5 Due Friday 11/3 for period 6 Secondary assignment: workbook pg 119 evens; pg 120 #13, 15, 17; 122 #4-6

3-6 Workbook Assignments (Standard) Primary Assignment: pg 119 #1 – 9 odds, pg120 #12 – 18 evens, 19, pg121 # 5 – 9 Due Friday 11/3 Secondary assignment: workbook pg 119 evens; pg 120 #13, 15, 17