# 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. #### Questions & Answers (1+cosA)(1-cosA)=sin^2A BINCY Reply good Neha why I'm sending you solved question Mirza Teach me abt the echelon method Khamis exact value of cos(π/3-π/4) Ankit Reply What is differentiation? Intakhab Reply modul questions trigonometry Thamarai Reply (1+cosA)(1-cosA)=sin^2A BINCY differentiate f(t)=1/4t to the power 4 +8 Jessica Reply I need trigonometry,polynomial duru Reply ok Augustine Why is 7 on top Bertha Reply simplify cot x / csc x Catherine Reply 👉🌹Solve🌻 Given that: cotx/cosx =cosx/sinx/cosx =1/sinx =cosecx Ans. Vijay what is the period of cos? SIYAMTHEMBA Reply your question might not seem clear as you asked. ask well to get perfect answers put your question on a table I'm willing to help you Mr Siyamthemba Patrick simplify: cot x/csc x Catherine sorry i didnt realize you were actually asking someone else to put their question on here. i thought this was where i was supposed to. Catherine some to dereve formula for bulky density kurash Solve Given that: cotx/cosx =cosx/sinx/cosx =1/sinx =cosecx Ans. Vijay if tan alpha + beta is equal to sin x + Y then prove that X square + Y square - 2 I got hyperbole 2 Beta + 1 is equal to zero Rahul Reply questions Thamarai ok AjA sin^4+sin^2=1, prove that tan^2-tan^4+1=0 SAYANTANI Reply what is the formula used for this question? "Jamal wants to save$54,000 for a down payment on a home. How much will he need to invest in an account with 8.2% APR, compounding daily, in order to reach his goal in 5 years?"
i don't need help solving it I just need a memory jogger please.
Kuz
A = P(1 + r/n) ^rt
Dale
how to solve an expression when equal to zero
its a very simple
Kavita
gave your expression then i solve
Kavita
Hy guys, I have a problem when it comes on solving equations and expressions, can you help me 😭😭
Thuli
Tomorrow its an revision on factorising and Simplifying...
Thuli
ok sent the quiz
kurash
send
Kavita
Hi
Masum
What is the value of log-1
Masum
the value of log1=0
Kavita
Log(-1)
Masum
What is the value of i^i
Masum
log -1 is 1.36
kurash
No
Masum
no I m right
Kavita
No sister.
Masum
no I m right
Kavita
tan20°×tan30°×tan45°×tan50°×tan60°×tan70°
jaldi batao
Joju
Find the value of x between 0degree and 360 degree which satisfy the equation 3sinx =tanx