# 4.3 Fitting linear models to data  (Page 7/14)

 Page 7 / 14

Determine whether the algebraic equation is linear. $\text{\hspace{0.17em}}6{x}^{2}-y=5$

Determine whether the function is increasing or decreasing.

$f\left(x\right)=7x-2$

Increasing

Determine whether the function is increasing or decreasing.

$g\left(x\right)=-x+2$

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

Passes through $\text{\hspace{0.17em}}\left(\text{7},\text{5}\right)\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}\left(\text{3},\text{17}\right)$

$y=-\text{3}x+\text{26}$

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

x -intercept at $\text{\hspace{0.17em}}\left(\text{6},0\right)\text{\hspace{0.17em}}$ and y -intercept at $\text{\hspace{0.17em}}\left(0,\text{1}0\right)$

Find the slope of the line shown in the graph.

3

Find the slope of the line graphed.

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

$y=\text{2}x-\text{2}$

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

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.

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 ?

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

$\begin{array}{c}2x-6y=12\\ -x+3y=1\end{array}$

parallel

$\begin{array}{c}y=\frac{1}{3}x-2\\ 3x+y=-9\end{array}$

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

$7x+9y=-63$

$\left(–9,0\right);\left(0,–7\right)$

$f\left(x\right)=2x-1$

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 $\text{\hspace{0.17em}}\left(5,11\right)\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}\left(10,1\right)$

Line 2: Passes through $\text{\hspace{0.17em}}\left(-1,3\right)\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}\left(-5,11\right)$

Line 1: $\text{\hspace{0.17em}}m=-2;$ Line 2: $\text{\hspace{0.17em}}m=-2;$ Parallel

Line 1: Passes through $\text{\hspace{0.17em}}\left(8,-10\right)\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}\left(0,-26\right)$

Line 2: Passes through $\text{\hspace{0.17em}}\left(2,5\right)\text{\hspace{0.17em}}$ and $\text{\hspace{0.17em}}\left(4,4\right)$

Write an equation for a line perpendicular to $\text{\hspace{0.17em}}f\left(x\right)=5x-1\text{\hspace{0.17em}}$ and passing through the point (5, 20).

$y=-0.2x+21$

Find the equation of a line with a y - intercept of $\text{\hspace{0.17em}}\left(0,2\right)\text{\hspace{0.17em}}$ and slope $\text{\hspace{0.17em}}-\frac{1}{2}.$

Sketch a graph of the linear function $\text{\hspace{0.17em}}f\left(t\right)=2t-5.$

Find the point of intersection for the 2 linear functions: $\text{\hspace{0.17em}}\begin{array}{c}x=y+6\\ 2x-y=13\end{array}.$

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?

More than 250

## Modeling with Linear Functions

Find the area of a triangle bounded by the y axis, the line $\text{\hspace{0.17em}}f\left(x\right)=10-2x,$ and the line perpendicular to $\text{\hspace{0.17em}}f\text{\hspace{0.17em}}$ that passes through the origin.

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

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, $\text{\hspace{0.17em}}t.\text{\hspace{0.17em}}$ When will no one be afflicted?

For the following exercises, use the graph in [link] showing the profit, $\text{\hspace{0.17em}}y,$ in thousands of dollars, of a company in a given year, $\text{\hspace{0.17em}}x,$ where $\text{\hspace{0.17em}}x\text{\hspace{0.17em}}$ represents years since 1980.

answer and questions in exercise 11.2 sums
what is a algebra
what is the identity of 1-cos²5x equal to?
__john __05
Kishu
Hi
Abdel
hi
Ye
hi
Nokwanda
C'est comment
Abdel
Hi
Amanda
hello
SORIE
Hiiii
Chinni
hello
Ranjay
hi
ANSHU
hiiii
Chinni
h r u friends
Chinni
yes
Hassan
so is their any Genius in mathematics here let chat guys and get to know each other's
SORIE
I speak French
Abdel
okay no problem since we gather here and get to know each other
SORIE
hi im stupid at math and just wanna join here
Yaona
lol nahhh none of us here are stupid it's just that we have Fast, Medium, and slow learner bro but we all going to work things out together
SORIE
it's 12
what is the function of sine with respect of cosine , graphically
tangent bruh
Steve
cosx.cos2x.cos4x.cos8x
sinx sin2x is linearly dependent
what is a reciprocal
The reciprocal of a number is 1 divided by a number. eg the reciprocal of 10 is 1/10 which is 0.1
Shemmy
Reciprocal is a pair of numbers that, when multiplied together, equal to 1. Example; the reciprocal of 3 is ⅓, because 3 multiplied by ⅓ is equal to 1
Jeza
each term in a sequence below is five times the previous term what is the eighth term in the sequence
I don't understand how radicals works pls
How look for the general solution of a trig function
stock therom F=(x2+y2) i-2xy J jaha x=a y=o y=b
sinx sin2x is linearly dependent
cr
root under 3-root under 2 by 5 y square
The sum of the first n terms of a certain series is 2^n-1, Show that , this series is Geometric and Find the formula of the n^th
cosA\1+sinA=secA-tanA
Wrong question
why two x + seven is equal to nineteen.
The numbers cannot be combined with the x
Othman
2x + 7 =19
humberto
2x +7=19. 2x=19 - 7 2x=12 x=6
Yvonne
because x is 6
SAIDI