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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

write down the polynomial function with root 1/3,2,-3 with solution
Gift Reply
if A and B are subspaces of V prove that (A+B)/B=A/(A-B)
Pream Reply
write down the value of each of the following in surd form a)cos(-65°) b)sin(-180°)c)tan(225°)d)tan(135°)
Oroke Reply
Prove that (sinA/1-cosA - 1-cosA/sinA) (cosA/1-sinA - 1-sinA/cosA) = 4
kiruba Reply
what is the answer to dividing negative index
Morosi Reply
In a triangle ABC prove that. (b+c)cosA+(c+a)cosB+(a+b)cisC=a+b+c.
Shivam Reply
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Aaron Reply
the polar co-ordinate of the point (-1, -1)
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prove the identites sin x ( 1+ tan x )+ cos x ( 1+ cot x )= sec x + cosec x
Rockstar Reply
tanh`(x-iy) =A+iB, find A and B
Pankaj Reply
B=Ai-itan(hx-hiy)
Rukmini
what is the addition of 101011 with 101010
Branded Reply
If those numbers are binary, it's 1010101. If they are base 10, it's 202021.
Jack
extra power 4 minus 5 x cube + 7 x square minus 5 x + 1 equal to zero
archana Reply
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
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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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