Slope-intercept form: y = mx + b

Ex. 1 Sketch THE graph for each equation

a. Y = 2x + 1 b. 3x + y = 5Y = -3x + 5

Slope of horizontal line:

Slope of vertical line:

0

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Slope of a line:xx

yy

Ex. 2 find the slope of the line passing through each pair of points

a. (-2, 0) and (3, 1)

b. (3, 4) and (3, 1)

5

1

23

01

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0

3

33

14

Point-slope form: y – y1 = m(x – x1)

Ex. 3 find the lope-intercept form of the equation of the line that has slope of 5 and goes through (4, -7)

Y – –7 = 5(x – 4)

Y + 7 = 5x – 20

Y = 5x – 27

Slope of parallel lines:

Slope of perpendicular lines:

same

neg. reciprocal

Ex. 4 Find the slope-intercept forms of the equations of the lines that pass through the point (3, -5) and are (a) parallel and (b) perpendicular to the line 2x – 3y = 5

2x – 3y = 5

– 3y = –2x + 5

y = 2/3x + 5/3 (A) Parallel

y – – 5 = 2/3(x – 3)

y + 5 = 2/3x – 2

y = 2/3x – 7

(B) Perpendicular

y – – 5 = –3/2(x – 3)

y + 5 = –3/2x + 9/2

y = –3/2x – 1/2

Ex. 5 The maximum recommended slope of a wheelchair ramp is 1/12. A business is installing a wheelchair ramp that rises 22 inches over a horizontal length of 24 feet. Is the ramp steeper than recommended?

Ex. 7 A college purchased exercise equipment worth $12,000 for the new campus fitness center. The equipment has a useful life of 8 years. The salvage value at the end of 8 years is $2000. Write a linear equation that describes the book value of the equipment each year.

076.0288

22

in

in

changehorizontal

changeverticalslope

1/12 = 0.0833 Ramp is not steeper

1250$8

10000

80

200012000

slope

(0, 12000) and (8, 2000) V – 12000 = –1250(t – 0)

V = –1250t + 12000

Ex. 8 The sales per share for Starbucks Corporation were $6.97 in 2001 and $8.47 in 2002. Using only this information, write a linear equation that gives the sales per share in terms of the year. The predict the sales per share for 2003.

5.11

5.1

12

97.647.8

slope

(1, 6.97) and (2, 8.47) y – 6.97 = 1.5(x – 1)

y = 1.5x + 5.47

y = 1.5(3) + 5.47

y = 9.97

$ 9.97 per share in 2003 (estimate based on our equation)

$ 10.35 per share in 2003 (actual)