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Determine whether the function is increasing or decreasing.

g ( x ) = x + 2

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Given each set of information, find a linear equation that satisfies the given conditions, if possible.

Passes through ( 7 , 5 ) and ( 3 , 17 )

y = 3 x + 26

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Given each set of information, find a linear equation that satisfies the given conditions, if possible.

x -intercept at ( 6 , 0 ) and y -intercept at ( 0 , 1 0 )

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Find the slope of the line shown in the line graph.

3

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Find the slope of the line graphed.

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Write an equation in slope-intercept form for the line shown.

y = 2 x 2

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Does the following table represent a linear function? If so, find the linear equation that models the data.

x –4 0 2 10
g ( x ) 18 –2 –12 –52
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Does the following table represent a linear function? If so, find the linear equation that models the data.

x 6 8 12 26
g ( x ) –8 –12 –18 –46

Not linear.

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On June 1 st , a company has $4,000,000 profit. If the company then loses 150,000 dollars per day thereafter in the month of June, what is the company’s profit n th day after June 1 st ?

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Graphs of Linear Functions

For the following exercises, determine whether the lines given by the equations below are parallel, perpendicular, or neither parallel nor perpendicular:

2 x 6 y = 12 x + 3 y = 1

parallel

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y = 1 3 x 2 3 x + y = 9

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For the following exercises, find the x - and y - intercepts of the given equation

7 x + 9 y = −63

( –9 , 0 ) ; ( 0 , –7 )

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For the following exercises, use the descriptions of the pairs of lines to find the slopes of Line 1 and Line 2. Is each pair of lines parallel, perpendicular, or neither?

  • Line 1: Passes through ( 5 , 11 ) and ( 10 , 1 )
  • Line 2: Passes through ( −1 , 3 ) and ( −5 , 11 )

Line 1: m = 2 ; Line 2: m = 2 ; Parallel

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  • Line 1: Passes through ( 8 , −10 ) and ( 0 , −26 )
  • Line 2: Passes through ( 2 , 5 ) and ( 4 , 4 )
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Write an equation for a line perpendicular to f ( x ) = 5 x 1 and passing through the point (5, 20).

y = 0.2 x + 21

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Find the equation of a line with a y - intercept of ( 0 ,   2 ) and slope 1 2 .

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Sketch a graph of the linear function f ( t ) = 2 t 5 .

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Find the point of intersection for the 2 linear functions: x = y + 6 2 x y = 13

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A car rental company offers two plans for renting a car.

  • Plan A: 25 dollars per day and 10 cents per mile
  • Plan B: 50 dollars per day with free unlimited mileage

How many miles would you need to drive for plan B to save you money?

250.

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Modeling with Linear Functions

Find the area of a triangle bounded by the y axis, the line f ( x ) = 10 2 x , and the line perpendicular to f that passes through the origin.

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A town’s population increases at a constant rate. In 2010 the population was 55,000. By 2012 the population had increased to 76,000. If this trend continues, predict the population in 2016.

118,000.

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The number of people afflicted with the common cold in the winter months dropped steadily by 50 each year since 2004 until 2010. In 2004, 875 people were inflicted.

Find the linear function that models the number of people afflicted with the common cold C as a function of the year, t . When will no one be afflicted?

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For the following exercises, use the graph in [link] showing the profit, y , in thousands of dollars, of a company in a given year, x , where x represents years since 1980.

Find the linear function y , where y depends on x , the number of years since 1980.

y = 3 00 x + 11 , 5 00

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Questions & Answers

what is the diameter of(x-2)²+(y-3)²=25
Den Reply
how to solve the Identity ?
Barcenas Reply
what type of identity
Jeffrey
Confunction Identity
Barcenas
For each year t, the population of a forest of trees is represented by the function A(t) = 117(1.029)t. In a neighboring forest, the population of the same type of tree is represented by the function B(t) = 86(1.025)t.
Shakeena Reply
by how many trees did forest "A" have a greater number?
Shakeena
32.243
Kenard
how solve standard form of polar
Rhudy Reply
what is a complex number used for?
Drew Reply
It's just like any other number. The important thing to know is that they exist and can be used in computations like any number.
Steve
I would like to add that they are used in AC signal analysis for one thing
Scott
Good call Scott. Also radar signals I believe.
Steve
They are used in any profession where the phase of a waveform has to be accounted for in the calculations. Imagine two electrical signals in a wire that are out of phase by 90°. At some times they will interfere constructively, others destructively. Complex numbers simplify those equations
Tim
Is there any rule we can use to get the nth term ?
Anwar Reply
how do you get the (1.4427)^t in the carp problem?
Gabrielle Reply
A hedge is contrusted to be in the shape of hyperbola near a fountain at the center of yard.the hedge will follow the asymptotes y=x and y=-x and closest distance near the distance to the centre fountain at 5 yards find the eqution of the hyperbola
ayesha Reply
A doctor prescribes 125 milligrams of a therapeutic drug that decays by about 30% each hour. To the nearest hour, what is the half-life of the drug?
Sandra Reply
Find the domain of the function in interval or inequality notation f(x)=4-9x+3x^2
prince Reply
hello
Jessica Reply
Outside temperatures over the course of a day can be modeled as a sinusoidal function. Suppose the high temperature of ?105°F??105°F? occurs at 5PM and the average temperature for the day is ?85°F.??85°F.? Find the temperature, to the nearest degree, at 9AM.
Karlee Reply
if you have the amplitude and the period and the phase shift ho would you know where to start and where to end?
Jean Reply
rotation by 80 of (x^2/9)-(y^2/16)=1
Garrett Reply
thanks the domain is good but a i would like to get some other examples of how to find the range of a function
bashiir Reply
Practice Key Terms 5

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Source:  OpenStax, Precalculus. OpenStax CNX. Jan 19, 2016 Download for free at https://legacy.cnx.org/content/col11667/1.6
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