Slope-intercept form: y = mx + b

Ex. 1 Sketch THE graph for each equation a. Y = 2x + 1 b. 3x + y = 5 Y = -3x + 5

Slope of horizontal line: 0 Slope of vertical line: undefined Slope of a line:

y x

 

y x

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)

1  0 3   2  1 5 4  1 3  3  3 0 

undefined

Point-slope form: y – y

1

= m(x – x

1

)

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: same Slope of perpendicular lines: 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 (B) Perpendicular y – – 5 = –3/2(x – 3) y + 5 = –3/2x + 9/2 y – – 5 = 2/3(x – 3) y + 5 = 2/3x – 2 y = –3/2x – 1/2 y = 2/3x – 7

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?

1/12 = 0.0833

Ramp is not steeper

slope  vertical horizontal change change  22 in 288 in  0 .

076

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.

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

slope  12000  2000 0  8  10000  8   $ 1250

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.

(1, 6.97) and (2, 8.47)

slope  8 .

47  6 .

97 2  1  1 .

5 1  1 .

5

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)