Find the value of r so the line that passes through each pair of points has the given slope.

40. In 1991, the federal minimum wage rate was $4.25 per hour. In 1997, it was increased to $5.15. Find the annual rate of change in the federal minimum wage rate from 1991 to 1997.

41. (6,2), (9,r), m=-1

42. (4,-5), (3,r), m=8

43. (5,r), (2,-3), m=4/3

44. (-2,7), (r,3), m=4/3

45. (1/2, -1/4), (r,-5/4), m=4

46. (2/3, r), (1,1/2), m= 1/2

47. (4,r), (r,2), m=-5/3

48. (r, 5), (-2, r), m=-2/9

Question

kels00 kels00

02-12-2014
Mathematics

Answered

Find the value of r so the line that passes through each pair of points has the given slope.

40. In 1991, the federal minimum wage rate was $4.25 per hour. In 1997, it was increased to $5.15. Find the annual rate of change in the federal minimum wage rate from 1991 to 1997.

41. (6,2), (9,r), m=-1

42. (4,-5), (3,r), m=8

43. (5,r), (2,-3), m=4/3

44. (-2,7), (r,3), m=4/3

45. (1/2, -1/4), (r,-5/4), m=4

46. (2/3, r), (1,1/2), m= 1/2

47. (4,r), (r,2), m=-5/3

48. (r, 5), (-2, r), m=-2/9

Answer :

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Slope is rise over run.
40. the rise is $0.90 and the run is 6 years, so the annual rate of change is .9/6 = $0.15 per year
40) Final answer: $0.15 per year

For 41-48, find the difference between the given values of the same variable, then multiply by the slope and add/subtract from the variable whose second value is missing (sorry if that's confusing)
41. 9-6=3 => 3*(-1)=-3 => 2+3=-1
41) Final answer: r=-1
42. 4-3=1 => 1*8=8 => (-5)-8=-13
42) Final answer: r=-13
43. 5-2=3 => 3*(4/3)=4 => -3+4=1
43) Final answer: r=1
44. 7-3=4 => 4*(3/4)=3 (flip the slop to find x values) => -2-3=-5
44) Final answer: r=-5
45. (-1/4)-(-5/4)=4/4=1 => 1*(1/4)=1/4 (again flip the slope) => 1/2-1/4=1/4
45) Final answer: r=1/4
46. 1-(2/3)=1/3 => (1/3)*(1/2)=(1/6) (don't have to flip this time) => (1/2)-(1/6)=1/3
46) Final answer: r=1/3
For 47 and 48, I'll setup an equation for r
47. (4-r)*(-5/3)=r-2 => -20/3+(5r)/3=r-2 => -14/3+(5r)/3=r => -14/3=-(2r)/3 => -14=-2r => r=7
47) Final answer: r=7
48. (R-(-2))*(-2/9)=5-r => -2(r+2)/9=5-r => -(2r)/9-4/9=5-r => -(2r)/9=49/9-r => (7r)/9=49/9 => 7r=49 => r=7
48) Final answer: r=7

Hope I helped :)