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# Several problems on finding slope, equation of line

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_____________________________________________________________________

1) 7- )
The slope is ________

The y-intercept is (0,____)

9) Find the slope, if it exists, of the line containing the pair of points.

(7,5) and (9,-4)
The slope m=_________
(Simplify your answer. Type an integer or a fiction. Type N if the slope is undefined)

10) Find the slope, if it exists, of the line containing the pair of points.
(-7,-19)and (-8,-20)
The slope m=____________
(Simplify your answer. Type an integer or a fiction. Type N if the slope is undefined)

20) Determine whether the graph of the pair of lines are parallel.
x+8=y
y-x=-4
What is the slope of the line x+8=y?_______________
What is the slope of the line y-x=-4?
Are the graphs of the given equations parallel?
Yes________ No_______________

21) Determine whether the graphs of each pair of lines are parallel.
2x+6=y
2y=4x-5
Are the graphs of the given equations parallel.

24) Find the slope-intercept equation of the line that has the given characteristics.
Slope 9 and y-intercept (0,8)
The slope-intercept equation is y=______________

25) Find the slope-intercept equation of the line that has the given characteristics.
Slope 5.9 and y-intercept (0,-3)
The slope-intercept equation y=_________________
(use intercept or dicimals for any numbers in the expression.)

26) Find an equation of the line having the given slope and containing the given point.
M=7,(6,1)
The equation of the line is y=____________
(Simplify your answer. Use integers or fractions for any number in the expression)

27) Find an equation of the line having the given slope and containing the given point.
m= ,(2,-2)
The equation of the line is y= _______________
(Simplify your answer. Use integers or fractions for any number in the expression)

28) Find the equation of the line containing the given pair of points. Express your answer in the form x=a,y=b, or y=mx+b
(-7,-7) and (4,4)
What is an equation of the line?

29) Find an equation of the line containing the given pair of points.
(-2,-4) and (-5,-6)
The equation of the line is y=_________.
(Simplify your answer. Use integers or fractions for any number in the expression)

30) Find an equation of the line containing the given pair of points.
[1/6,-1/3] and [5/6,3]
What is the equation of the line?
y=____________

31) Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y=mx+b
(6,7; x+6y=7
The equation of the line is y=___________
(Simplify your answer. Use integers or fractions for any numbers in the expression)

32) Write an equation of the line containing the given point and parallel to the given line.
(-9,2); 4x=5y+2
The equation of the line is y=_____________

(Simplify your answer. Use integers or fractions for any numbers in the expression)

33. Write an equation of the line containing the given point and perpendicular to the given line. Express your answer in the form y=mx+b
(2,4); 7x+y=6
The equation of the line is y=_______________
(Simplify your answer. Use integers or fractions for any numbers in the expression)

34. Write an equation of the line containing the given point and perpendicular to the given line.
(3,-3); 4x+5y=7
The equation of the line is y=_______________

The table lists data regarding the average salaries of several professional athletes in the year 1991 and 2001.
a) Use the data points to find a linear function that fits the data.
b) Use the function to predict the average salary in 2005 and 2010.
Year Average Salary
1991 \$277,000
2001 \$1,380,000
A linear function that fits the data is S(x)=_________________
(Let x= the number of years since 1990, and let S= the average salary x years from 1990)
The predicted average salary for 2005 is\$_____________
(Round to the nearest whole number)
The predicted average salary for 2010 is \$_______________
(Round to the nearest whole number)

37) In 1920, the record for a certain race was 45.4 sec. In 1980, it was 43.6 sec.
Let R(t)=the record in the race and t=the number of years since 1920.
a) Find a linear function that fits the data.
b) Use the function in(a) to predict the record in 2003 and in 2006.
c) Find the year when the record will be 42.5 sec
Find a linear function that fits the data.
R(t)=______________
(round to the nearest hundredth)
What is the predicted record for 2003?____________sec.
(round to the nearest tenth.)
What is the predicted record for 2006?_____________sec.
. (round to the nearest tenth.)
In what year the predicated record be 42.5 seconds?__________________
(round to the nearest year)

38) In 1991 the life expectancy of males in certain country was 64.9 years. In 1997, it was 68.4 years. Let E represent the life expectancy in year t and let t represents the number of years since 1991.
The linear function F(t) that fits the data is
E(t)=________t+____________.
(round to the nearest tenth.)
Use the function to predict the life expectancy of males in 2008.
E(17)=_________________
(round to the nearest tenth)

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#### Solution Summary

Step by step solutions to each problem is provided.

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## Word problems on Dental services, Retirement pay, Direct deposit, Bonus and taxes, Books and magazines

Question 1
Dental services. The national cost C in billions of dollars for dental services can be modeled by the linear equation

C = 2.85n +30.52,

Where n is the number of years since 1990 (Health Care Financing Administration, www.hcfa.gov).
a) Find and interpret the C-intercept for the line.
b) Find and interpret the n-intercept for the line.
c) Graph the line for n ranging from 0 through 20
d) If this trend continues, then in what year will the cost of dental services reach 100 billion?

Question 2
64. Retirement pay. The annual Social Security benefit of a retiree depends on the age at the time of retirement. The accompanying graph gives the annual benefit for persons retiring at ages 62 through 70 in the year 2005 or later (Social Security Administration, www.ssa.gov). What is the annual benefit for a person who retires at age 64? At what retirement age does a person receive an annual benefit of\$11,600? Find the slope of each line segment on the graph, and interpret your results. Why do people who postpone retirement until 70 years of age get the highest benefit?
(Retirement age, Annual Social Security benefit (dollars))
(62, 7000)
(64, 8000)
(67, 10,000)
(70, 12,400)

Question 3
80. Direct deposit. The percentage of workers receiving direct deposit of their paychecks went from 32% in 1994 to 60% in 2004 (www.directdeposit.com). Let 1994 be year 0 and
2004 be year 10.
a) Write the equation of the line through (0, 32) and (10, 60) to model the growth of direct deposit.
b) Use the accompanying graph to predict the year in which 100% of all workers will receive direct deposit of their paychecks.
c) Use the equation from part (a) to predict the year in which 100% of all workers will receive direct deposit

Question 4
Graph each inequality
2x<3y+6
Graph must be in excel format with shade.

Question 5
Bonus and taxes. A company has an income of \$100,000 before paying taxes and a bonus. The bonus B is to be 20% of the income after deducting income taxes T but before deducting the bonus. So
B =0.20(100,000 -T ).
Because the bonus is a deductible expense, the amount of income tax T at a 40% rate is 40% of the income after deducting the bonus. So
T = 0.40(100,000 - B).
a) Use the accompanying graph to estimate the values of T and B that satisfy both equations.
b) Solve the system algebraically to find the bonus and the amount of tax.

Question 6

Books and magazines. At Gwen's garage sale, all books were one price, and all magazines were another price. Harriet bought four books and three magazines for \$1.45, and June bought two books and five magazines for \$1.25.
What was the price of a book and what was the price of a magazine?

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