Download presentation

Presentation is loading. Please wait.

Published byJack Lawson Modified over 2 years ago

1

2
Point Slope Math 374

3
Topic Box 1) Slope 1) Slope 2) Word Problems 2) Word Problems - keys - Point – Point - Slope – Point - Y Int – Point - Slope – Y int

4
The Slope We know that we are dealing with linear functions We know that we are dealing with linear functions y = mx + b y = mx + b Slope y int The slope is not always obvious, if we do not know the equation

5
Understanding the Slope What makes a slope? What makes a slope? Rise Run We define the slope as the ratio between the rise and the run Slope = m = rise run

6
Formula for Slope If we have two points (x 1, y 1 ) (x 2, y 2 ) If we have two points (x 1, y 1 ) (x 2, y 2 ) Slope = m = y 1 – y 2 = y 2 – y 1 Slope = m = y 1 – y 2 = y 2 – y 1 x 1 – x 2 x 2 – x 1 Remember it is Y over X! Remember it is Y over X! Maintain order Maintain order

7
Calculating Slope Slope = m = y 1 – y 2 = y 2 – y 1 Slope = m = y 1 – y 2 = y 2 – y 1 x 1 – x 2 x 2 – x 1 x 1 – x 2 x 2 – x 1 (5, 4) (2, 1) (5, 4) (2, 1) m = 1 m = 1 (x 1,y 1 ) (x 2,y 2 )

8
Ex # 2 A = (-4, 2) B=(2, -4) (x 1,y 1 ) (x 2,y 2 ) -4 – m = -1

9
(4, 5) (1, 1) Ex #3 (x 2,y 2 ) (x 1,y 1 ) 1 – 5 1 – 4 m = -4 -3

10
Two Decimal Place Practice Find the slope of (4,217.08) (11,575.41) Find the slope of (4,217.08) (11,575.41) m = – m = –

11
Word Problems BASICS Set your x and y Set your x and y Find the linear function meaning find slope – m and y int or b Find the linear function meaning find slope – m and y int or b Solve question Solve question x is always time x is always time y is always money y is always money

12
Word Problems Cont KEYS Per Per Rate Rate m Fixed Initial b Point – two values point

13
Point – Point Little Billy rents a car for 5 days and pays $ Little Sally rents a car for 14 days and pays $ Little Billy rents a car for 5 days and pays $ Little Sally rents a car for 14 days and pays $ a) How much would it cost to rent a car for 27 days? b) How many days can you get for $ Step 1: Set Your x and y… what are they?

14
Solution x is # of days x is # of days y is $ (money) y is $ (money) (5, ) (14, ) (5, ) (14, ) m = – m = – – 14 5 – 14 m = m = y = 82.73x + b y = 82.73x + b

15
Solution Cont (5, ) = 82.73(5) + b (5, ) = 82.73(5) + b = b = b 50 = b 50 = b b = 50 b = 50 y = 82.73x + 50 y = 82.73x + 50 A) x = 27 y = (27) + 50 A) x = 27 y = (27) + 50 y = $ y = $

16
Solution Cont b) y = = 82.73x + 50 b) y = = 82.73x = 82.73x = 82.73x 30 = x 30 = x x = 30 x = 30

17
Slope Point Little Billy rents a car and pays a rate of $43.91 per day. Little Sally rents for 42 days and pays $ Little Billy rents a car and pays a rate of $43.91 per day. Little Sally rents for 42 days and pays $ a) How much would it cost to rent a car for 27 days? a) How much would it cost to rent a car for 27 days? b) How many days can you get for $ ? b) How many days can you get for $ ? Step 1: Set your x and y Step 1: Set your x and y

18
Solution x is # of days x is # of days y is $ (money) y is $ (money) m = $43.91 (42, ) m = $43.91 (42, ) y = 43.91x + b y = 43.91x + b (42, ) = (42) + b (42, ) = (42) + b = b = b = b = b b = b = 56.23

19
Solution Cont y = 43.91x y = 43.91x A) x = 27 y = (27) A) x = 27 y = (27) y = $ y = $ B) y = =4391 x B) y = =4391 x = 43.91x = 43.91x 55 = x 55 = x x = 55 x = 55

20
Y Int - Point Little Billy rents a car and pays a fixed cost of $ Little Sally rents for 12 days and pays $ Little Billy rents a car and pays a fixed cost of $ Little Sally rents for 12 days and pays $ a) How much for 27 days? a) How much for 27 days? b) How many days for $1232? b) How many days for $1232? x is # of days x is # of days y is $ money y is $ money b = (12, ) b = (12, ) y = mx y = mx

21
Solution (12, ) =12m (12, ) =12m = 12m = 12m = m = m m = m = y = 99.99x y = 99.99x a) x = 27 y = (27) a) x = 27 y = (27) y = $ y = $

22
Solution (Cont) B) y = = 99.99x B) y = = 99.99x = 99.99x = 99.99x 11 = x 11 = x x = 11 x = 11

23
Slope – Y int Little Billy rents a car and pays a rate of $73.99 per day. Little Sally pays a fixed cost of $42.19 Little Billy rents a car and pays a rate of $73.99 per day. Little Sally pays a fixed cost of $42.19 a) How much for 27 days? a) How much for 27 days? b) How many days for $ b) How many days for $ x is # of days x is # of days y is $ (money) y is $ (money) m = b = m = b = y = 73.99x y = 73.99x

24
Solutions x= 27 y = (27) x= 27 y = (27) y = y = b) y = = 73.99x b) y = = 73.99x = 73.99x = 73.99x 5 = x 5 = x x = 5 x = 5

Similar presentations

© 2016 SlidePlayer.com Inc.

All rights reserved.

Ads by Google