Slope Between Two Points

Table of Contents 8: Warm-Up, Guided Practice 9: How Do I Find the Slope Between Two Points?

Warm Up Write a symbolic representation based on the verbal representation. 1. A cab company chargers a $5 boarding rate in addition to its meter which is $3 for every mile. Write the symbolic representation where C is the total charge and m is the number of miles driven.

Learning Intention/Success Criteria LI: We are learning to find the slope between two points SC: I know how to -graph linear functions represented symbolically as f(x) = mx + b -identify m and b and understand what it means -interpret what m means in context -find m from a table, graph, or ordered pairs -understand how the slope formula relates to numerical and visual representation

EQ: How Do I Find the Slope Between Two Points? 5/14/2019

Slope A number used to indicate the steepness of a line and if the line is tilted uphill or downhill Represented by the letter “m” m = change in y change in x Slope Formula m = y2 – y1 x2 – x1

Example 1: Find the slope between two points: (3, -4) and (2, 5) (3, -4) and (2, 5) (x1, y1) (x2, y2) m = y2 – y1 x2 – x1 m = 5 – -4 2 – 3 m = 5 + 4 2 – 3 m = 9 -1 = -9

(3, -4) and (2, 5) Proof (2, 5) Rise Run -9 1 -9 1 (3, -4)

Guided Practice 1 Find the slope between the two points: (-4, 2) and (-6, -8)

Guided Practice 1 Poll Find the slope between the two points: (-4, 2) and (-6, -8) A] 5 B] -5 C] 2 D] 1/5

Guided Practice 1 Answer Find the slope between the two points: (-4, 2) and (-6, -8) m = y2 – y1 x2 – x1 m = -8 - 2 -6 + 4 m = -10 -2 m = -8 - 2 -6 - - 4 = 5

Guided Practice 2 Find the slope between the two points: (8, -3) and (0, -1)

Guided Practice 2 Poll Find the slope between the two points: (8, -3) and (0, -1) A] 1/3 B] -1/4 C] -4 D] -3

Guided Practice 2 Answer Find the slope between the two points: (8, -3) and (0, -1) m = y2 – y1 x2 – x1 m = -1 + 3 0 - 8 m = 2 -8 m = -1 - - 3 0 - 8 = -1/4

Example 2: Find the slope between two points: (5, 4) and (5, 1) (5, 4) and (5, 1) (x1, y1) (x2, y2) m = y2 – y1 x2 – x1 m = 1 - 4 5 - 5 m = -3 0 m = undefined

Guided Practice 3 Find the slope between the two points: (-6, 3) and (-7, 3)

Guided Practice 3 Poll Find the slope between the two points: (-6, 3) and (-7, 3) A] 4/3 B] 3/4 C] undefined D] zero

Guided Practice 3 Answer Find the slope between the two points: (-6, 3) and (-7, 3) m = y2 – y1 x2 – x1 m = 3 - 3 -7 - 6 m = 0 -13 m = 3 - 3 -7 - - 6 = 0

Guided Practice 4 Find the slope between the two points: (-1, -3) and (-1, -5)

Guided Practice 4 Poll Find the slope between the two points: (-1, -3) and (-1, -5) A] 2/3 B] 1 C] undefined D] zero

Guided Practice 4 Answer Find the slope between the two points: (-1, -3) and (-1, -5) m = y2 – y1 x2 – x1 m = -5 + 3 -1 + 1 m = -2 0 m = -5 - - 3 -1 - - 1 = undefined

Example 3: The table shows the number of miles a plane traveled while in flight. Use the table to find the rate of change. Time (min) Distance (mi) 30 290 60 580 90 870 120 1160 x1 y1 x2 y2 m = y2 – y1 x2 – x1 m = 580 60 m = 870 - 290 90 - 30 m = 9.66

What does the slope mean in context? y x Miles flown Minutes flying 9.66 1 Miles flown Minutes flying The plane flies 9.66 miles every minute.

Guided Practice 5 The table below shows the number of small packs of fruit snacks, F(b), per box, b. Find the slope of the line and explain what it means in context. Boxes (b) 3 5 7 9 Packs, F(b) 24 40 56 72

Guided Practice 5 Poll Find the slope of the table A] -8 B] -1/8 C] 8 D] 1/8

Guided Practice 5 Answers Find the slope of the table x2 x1 Boxes (b) 3 5 7 9 Packs, F(b) 24 40 56 72 m = y2 – y1 x2 – x1 y2 y1 m = 8 m = 48 6 m = 72 - 24 9 - 3 There are 8 packs per box