lecture 1.2 line

8/7/2019 Lecture 1.2 Line

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1: Lines

Learning Goals:Find slopes of lines including

parallel & perpendicularDescribe connection between

arithmetic sequences & linesGraph linesWrite equations of lines



Try This

A lecture hall has 6 seats inthe 1st row, 8 in the 2nd, 10in the 3rd and so on throughrow 12. Rows 12 through 20(the last row) all have the

same number of seats. Findthe number of seats in thehall.

428



Important Idea

In an arithmetic sequence,when each term is pairedwith its position n, theordered pairs form a discrete

function whose domain is theset of counting numbers.

nu



Ex ample

_ a3,5,7,9,11,...

When n=1, =3 (1,3)1u

Whenn=

2,=5

(2,5)2

u

When n=3, =7 (3,7)1u

Domain isa CountingNumber

n

n

u



Important Idea

n

nu A line may

be drawn

through thediscretepoints toform acontinuous

function



Definition

Slope of a Line: If 1 1( , ) x y

& are points on theline, then the slope of theline through these points is

2 2( , ) x y

2 1

2 1

y y ym

x x x

( ! !

( 2 1, x x{



Try This

Find the slope

of the linethat passes

through(-2,5) and(3,-6)

11

5



Find the slope


through(0,1) and(-1,-3) 4

Try This



Find the slope


through(5,1) and(-1,1) 0

Try This



Find the slope

of the linethat passesthrough(5,1) and(5,7)

Undefined

Try This



Definition

Forms of Linear Equations: A x By c !

y x b!

1 1( ) y y m x x !

y b! x c!

StandardSlope Intercept

Point Slope

Horizontal Line Vertical Line



Definition

The slope intercept formof the equation of a line:

y x b!

slope y intercept



Try This

The first 3 terms of anarithmetic sequence are -2, 3& 8. Use the explicit form of

the sequence to express thenth term, and compare it tothe slope intercept form of the equation of the line that passes through the points on

the graph of the sequence.



Ex ample

Sketch the graph (do not use a calculator) of:

3 4 6 y x

!

Confirm your sketch with a

graphing calculator.



Try This

Sketch the graph (do not use a calculator) of:

Confirm your sketch with a

graphing calculator.

25

2 y x

!



Solution

51

2 y x!



Ex ampleFind the equation of thegraph with slope 2 that

passes through the point (-2,1). Write the equation inslope-intercept form.



Try This

Find the equation of thegraph with slope -1 that

passes through the point (0,-5). Write the equation inslope-intercept form.

5 y x!



Ex ample

Find the equation of the

line that passes throughthe points ( ,1) and(4,5).

2



Definition

Depreciation is an accounting

term which describes a lossof value with the passage of time.



Ex ample

A n office buys a new copierfor $8000. Four years laterits value is $2320. A ssumelinear depreciation.

a) Write the equation that represents value as afunction of years.



Ex ample

A n office buys a new copierfor $8000. Four years later

its value is $2320. A

ssumelinear depreciation.

b) Find its value 3 yearsafter it was purchased, that is, the y value when x=3.



Ex ample

A n office buys a new copierfor $8000. Four years later

its value is $2320. A

ssumelinear depreciation.

c) Graph the equation.



Ex ample

A n office buys a new copierfor $8000. Four years laterits value is $2320. A ssumelinear depreciation.

d) Find how many yearsbefore the system isworthless, that is, the x value

when the y value is 0.



Definition

Two non-vertical lines areparallel if they have the

same slope. Two non-vertical lines are

perpendicular if theproduct of their slopes is-1.



Ex ampleGiven the line M whoseequation is ,

find the equation of the linesthrough the point (-4,2)

5 4 8 0 x y !

a. Parallel to M

b. Perpendicular to M



Try This

Given the line M

whoseequation is ,find the equation of the lines

through the point (-4,2)a. Parallel to M

3 2 6 0 x y !

b. Perpendicular to M

a.3

82

y x! b.2 2

3 3

y x!

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