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Find the equation of the line that passes through the following points:

( a ,   b ) and ( a ,   b + 1 )

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Find the equation of the line that passes through the following points:

( 2 a , b ) and ( a , b + 1 )

y = 1 2 x + b + 2

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Find the equation of the line that passes through the following points:

( a , 0 ) and ( c , d )

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Find the equation of the line parallel to the line g ( x ) = −0. 01 x +2 .01 through the point ( 1 , 2 ) .

y = –0.01 x + 2.01

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Find the equation of the line perpendicular to the line g ( x ) = −0. 01 x +2 .01 through the point ( 1 , 2 ) .

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For the following exercises, use the functions f ( x ) = −0. 1 x +200 and  g ( x ) = 20 x + 0.1.

Find the point of intersection of the lines f and g .

  ( 1999 201 , 400 , 001 2010 )

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Where is f ( x ) greater than g ( x ) ? Where is g ( x ) greater than f ( x ) ?

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Real-world applications

At noon, a barista notices that she has $20 in her tip jar. If she makes an average of $0.50 from each customer, how much will she have in her tip jar if she serves n more customers during her shift?

20 + 0.5 n

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A gym membership with two personal training sessions costs $125, while gym membership with five personal training sessions costs $260. What is cost per session?

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A clothing business finds there is a linear relationship between the number of shirts, n , it can sell and the price, p , it can charge per shirt. In particular, historical data shows that 1,000 shirts can be sold at a price of $ 30 , while 3,000 shirts can be sold at a price of $22. Find a linear equation in the form p ( n ) = m n + b that gives the price p they can charge for n shirts.

p ( n ) = 0.004 n + 34

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A phone company charges for service according to the formula: C ( n ) = 24 + 0.1 n , where n is the number of minutes talked, and C ( n ) is the monthly charge, in dollars. Find and interpret the rate of change and initial value.

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A farmer finds there is a linear relationship between the number of bean stalks, n , she plants and the yield, y , each plant produces. When she plants 30 stalks, each plant yields 30 oz of beans. When she plants 34 stalks, each plant produces 28 oz of beans. Find a linear relationships in the form y = m n + b that gives the yield when n stalks are planted.

y = 0.5 n + 45

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A city’s population in the year 1960 was 287,500. In 1989 the population was 275,900. Compute the rate of growth of the population and make a statement about the population rate of change in people per year.

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A town’s population has been growing linearly. In 2003, the population was 45,000, and the population has been growing by 1,700 people each year. Write an equation, P ( t ) , for the population t years after 2003.

P ( t ) = 1700 t + 45 , 000

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Suppose that average annual income (in dollars) for the years 1990 through 1999 is given by the linear function: I ( x ) = 1054 x + 23 , 286 , where x is the number of years after 1990. Which of the following interprets the slope in the context of the problem?

  1. As of 1990, average annual income was $23,286.
  2. In the ten-year period from 1990–1999, average annual income increased by a total of $1,054.
  3. Each year in the decade of the 1990s, average annual income increased by $1,054.
  4. Average annual income rose to a level of $23,286 by the end of 1999.
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When temperature is 0 degrees Celsius, the Fahrenheit temperature is 32. When the Celsius temperature is 100, the corresponding Fahrenheit temperature is 212. Express the Fahrenheit temperature as a linear function of C , the Celsius temperature, F ( C ) .

  1. Find the rate of change of Fahrenheit temperature for each unit change temperature of Celsius.
  2. Find and interpret F ( 28 ) .
  3. Find and interpret F ( –40 ) .
  1. Rate of change = Δ F Δ C = 212 32 100 0 = 1.8  degrees F for one degree change in C
  2. F ( 28 ) = 1.8 ( 28 ) + 32 = 82.4  degrees F is 28 degrees C
  3. F ( 40 ) = 1.8 ( 40 ) + 32 = 40  degrees F is -40 degrees C
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Questions & Answers

the gradient function of a curve is 2x+4 and the curve passes through point (1,4) find the equation of the curve
Kc Reply
1+cos²A/cos²A=2cosec²A-1
Ramesh Reply
test for convergence the series 1+x/2+2!/9x3
success Reply
a man walks up 200 meters along a straight road whose inclination is 30 degree.How high above the starting level is he?
Lhorren Reply
100 meters
Kuldeep
Find that number sum and product of all the divisors of 360
jancy Reply
answer
Ajith
exponential series
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what is subgroup
Purshotam Reply
Prove that: (2cos&+1)(2cos&-1)(2cos2&-1)=2cos4&+1
Macmillan Reply
e power cos hyperbolic (x+iy)
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10y
Michael
tan hyperbolic inverse (x+iy)=alpha +i bita
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prove that cos(π/6-a)*cos(π/3+b)-sin(π/6-a)*sin(π/3+b)=sin(a-b)
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why {2kπ} union {kπ}={kπ}?
Huy Reply
why is {2kπ} union {kπ}={kπ}? when k belong to integer
Huy
if 9 sin theta + 40 cos theta = 41,prove that:41 cos theta = 41
Trilochan Reply
what is complex numbers
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Solve 2cos x + 3sin x = 0.5
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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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