1. 2.2: Equations of Lines October 2, 2009

2. P. 82-87, #1-10 1)Exact 2)Approximate 3)Approximate 4)Exact 5)a) m=2, b=-1, xint=0.5 b) f(x)=2x-1 c) 0.5 6) a) m= -2, b= 1, xint=0.5 b) f(x)=-2x+1c) 0.5 7) a) m=3/4, b= -3, xint=4 b) f(x)= 3/4x -3c) 4 8) a) m=-1/3, b= 2, xint=6 b) f(x)=-1/3x+2c) 6 9) a) m=20, b= -50, xint=2.5 b) f(x)=20x-50c) 2.5 10) a) m=-200, b= 300, xint= 1.5 b) f(x)= -200x+300c) 1.5

3. P. 82-87, #25-30, 41 25)f(x)= -3/4x+1/3 26)f(x)= -122x+805 27)f(x)= 15x 28) f(x)= 1.68x+1.23 29)f(x)= 0.5x+4 30)f(x)= -2x+3 41) a) f(x)= 6x+200 b) 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

4. P. 82-87, #42-48 42) a) f(x)=5.8x+47 b) 93,400,000 43) a) f(x)=16.7-0.26x b) f(12)=13.58 44) a) 180,956 gallons b) g(x)= 180,956/231(x) c) 1958 gallons d) 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}

5. P. 82-87, #49-51, 57-61 49) f(x)=3x-7 50) f(x)= -1.4x-3.1 51) f(x) = -2.5x 57) a) positive b) y=3.0929x-2.2143 c) y=5.209 58) a) positive b) y=0.985x+5.02 c) y=7.384 59) a) negative b) y= -2.8857x+9.3254 c) y= -0.00028 60) a) negative b) y=-2.9867x+24.92 c) y=17.752 61) b) y=14.680x+277.82 c) 2500 light years

6. 62-64 62) a) y=0.0349x+0.9905 b) About 2.74 minutes 63) b) y=0.6301x-1236.4 c) 0.63% on average 64) b) negative c) y=-0.019x+39.66 d) 2.98

9. 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.

10. Point-slope form y-y 1 =m(x-x 1 ) y=m(x-x 1 )+y 1 Where m= slope and (x 1,y 1 ) is an ordered pair on the line.

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

13. Slope-intercept y=mx+b Where m=slope and b=y-intercept.

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

15. 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.

16. Intercept form x+ y = 1 a b Where a = x intercept and b=y intercept.

17. Change the following into slope- intercept form: x+ y = 1 2 -3

18. Horizontal and vertical lines Horizontal lines y=b Vertical lines x=k

19. Parallel and perpendicular Parallel: same slope Perpendicular: negative reciprocal slope (slopes multiply to be -1)

20. Finding perpendicular and parallel f(x) = 2x +1 – Parallel? – Perpendicular?

21. Finding perpendicular and parallel f(x)= ½x +1 – Parallel? – Perpendicular?

22. 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 X2345 y1.11.82.53.2

23. Direct variation y=kx Where k does not equal zero. k is called the constant of proportionality or constant of variation.

24. Your assignment P. 99-105 2-18 even 26-46 even 53-56 all 66-78 even 86, 88