2.2: Equations of Lines

October 2, 2009

P. 82-87, #1-10

1) Exact2) Approximate3) Approximate4) Exact5) a) m=2, b=-1, xint=0.5b) f(x)=2x-1c) 0.56) a) m= -2, b= 1, xint=0.5b) f(x)=-2x+1 c) 0.5

7) a) m=3/4, b= -3, xint=4b) f(x)= 3/4x -3 c) 48) a) m=-1/3, b= 2, xint=6b) f(x)=-1/3x+2 c) 69) a) m=20, b= -50, xint=2.5b) f(x)=20x-50 c) 2.510) a) m=-200, b= 300,

xint= 1.5b) f(x)= -200x+300 c) 1.5

P. 82-87, #25-30, 41

25) f(x)= -3/4x+1/326) f(x)= -122x+80527) f(x)= 15x28) f(x)= 1.68x+1.2329) f(x)= 0.5x+430) f(x)= -2x+3

41) a) f(x)= 6x+200b) D = {x|0≤ x ≤ 50}c) yint=200, the tank

initially contained 200 gallons of fuel

d) Xint= -100/3, which corresponds to a negative time, which doesn’t make sense in this problem

P. 82-87, #42-48

42) a) f(x)=5.8x+47b) 93,400,00043) a) f(x)=16.7-0.26xb) f(12)=13.5844) a) 180,956 gallonsb) g(x)= 180,956/231(x)c) 1958 gallonsd) no, 2 downspouts

45) f(x)=3x, x represents seconds; D={x|0 ≤x ≤3}

46) f(x)=30-3/2x, x represents seconds; D={x|0 ≤x ≤20}

47) f(x)=21.5+0.581x; x equals years after 1900; D={x|0 ≤x ≤100}

48) f(x)=8.3-0.32x, x is years after 1992; D={x|0 ≤x ≤0}

P. 82-87, #49-51, 57-61

49) f(x)=3x-750) f(x)= -1.4x-3.151) f(x) = -2.5x57) a) positiveb) y=3.0929x-2.2143c) y=5.20958) a) positiveb) y=0.985x+5.02c) y=7.384

59) a) negativeb) y= -2.8857x+9.3254c) y= -0.0002860) a) negativeb) y=-2.9867x+24.92c) y=17.75261) b) y=14.680x+277.82c) 2500 light years

62-64

62) a) y=0.0349x+0.9905b) About 2.74 minutes63) b) y=0.6301x-1236.4c) 0.63% on average64) b) negativec) y=-0.019x+39.66d) 2.98

Objectives

• Write point-slope and slope-intercept form for a line.

• Find the intercepts of a line.• Write the equations for horizontal, vertical,

parallel, and perpendicular lines.• Understand interpolation and extrapolation.• Use direct variation to solve problem.

Point-slope form

y-y1=m(x-x1)

y=m(x-x1)+y1

Where m= slope and (x1,y1) is an ordered pair on the line.

Find a line that passes through the following points (2, 3), (3,7).

Slope-intercept

y=mx+bWhere m=slope and b=y-intercept.

Find a line that passes through (-1, 5), (-2, 7) in point-slope form and covert it to

slope-intercept form.

X-intercept and y-intercept

• To find the x-intercept, solve for x when for y=0.

• To find the y-intercept, solve for y when x=0.

Intercept form

x + y = 1a bWhere a = x intercept and b=y intercept.

Change the following into slope-intercept form:x + y = 12 -3

Horizontal and vertical lines

• Horizontal linesy=b

• Vertical linesx=k

Parallel and perpendicular

• Parallel: same slope• Perpendicular: negative reciprocal slope

(slopes multiply to be -1)

Finding perpendicular and parallel

• f(x) = 2x +1– Parallel?– Perpendicular?

Finding perpendicular and parallel

• f(x)= ½x +1– Parallel?– Perpendicular?

Interpolation and extrapolation

• Interpolation: estimate values between two known values

• Extrapolation: estimate values that are not between two known values

• Predict y when x=2.5• Predict y when x=6

X 2 3 4 5

y 1.1 1.8 2.5 3.2

Direct variation

y=kxWhere k does not equal zero.k is called the constant of proportionality or

constant of variation.

Your assignment

• P. 99-1052-18 even26-46 even53-56 all66-78 even86, 88