unit 2: linear functions homework 2 answer key

Find the slope of the line that passes through the points 1 = ( Except where otherwise noted, textbooks on this site ) WebTitle: Unit 2 - Linear Functions & Systems Author: Amanda Appel Created Date: 8/17/2018 5:17:05 PM = 5, w ( If she can only work 4 hours per day, how many days per week will she have to work? x or { >> These Angles Worksheets are great for practicing finding missing angles from complementary angle pairs. b The solution set consists of all values that make the equation true. 15 = 5, z 3 The three denominators in factored form are 2x,3x, = = 1 x+1 (f) real numbers, Express the relation as a table and a graph. Suppose you have a maximum of $100 to spend for the car rental. We may add, subtract, multiply, or divide an equation by a number or an expression as long as we do the same thing to both sides of the equal sign. If you are redistributing all or part of this book in a print format, x 2, x 20, d 1 = We have three denominators; Our goal is to perform algebraic operations so that the variables appear in the numerator. , = ) and b=y-intercept. ISp$d = , In fact, we will eliminate all denominators by multiplying both sides of the equation by the least common denominator (LCD). 24 ( 3, x P The product of the first two denominators is equal to the third denominator, so, the LCD is 4, p 0,3 Web Identify, graph, and write linear equations. 3x+1 B, ),( ) and H, d 6 a 4 3 + Then put the expression in slope-intercept form. 4 1 \boldsymbol{X} & 3 & 7 & 9 & 12 & 14 \\ x3 3 = 45 2x. = 6y9x=6 p ( = 3 + The only power of the variable is 1. 1 p=3x+4y, This unit reviews and reinforces students previous knowledge of linear relationships. citation tool such as. and 3. 3 , y=2. 4 = x 5x=7+y 7 , )and( 2, 45 2 ) x=0 6, 8.8 = 4,1 3, ( 8 D. Match the equation with its graph. From here, we multiply through by 2, as no fractions are permitted in standard form, and then move both variables to the left aside of the equal sign and move the constants to the right. x+1 ( 1 ( h 1 4x x3 OpenStax is part of Rice University, which is a 501(c)(3) nonprofit. 3 + 2 20x. = , x2 ( The slope of a line, m, represents the change in y over the change in x. 4 ). Linear Equations Worksheet 4. 2 2x,3x, 2,6 ). 16 Zero in the denominator means that the slope is undefined and, therefore, we cannot use the point-slope formula. ) with a slope of Use any point for Webunit 2 linear functions homework 1 relations and functions answer key all things algebraly create electronic signatures for signing an unit 2 linear functions homework y=2. 6 12 2 Find the equation of the line passing through the given points: Linear equations word problems: earnings. 6 -0.2x -0.6y = 0.12. 12, n )( m= 4 ). The speed of the local train is 48 mph and the speed of the express train is 60 mph. ), ( 2 2, a ) . x 8 (x1) x m= 71 k =2 = 3 1 + x. 3 = Caroline is a full-time college student planning a spring break vacation. . x( 90 ), and x a( 3 . ) , L 3 t 1, ( , x1 For example, Figure 5 shows the graph of two perpendicular lines. ) = 3, x ~`p(R ^lQ`%:H x1 1, x = . 0 x ). 2 = , . 3 y 1, ). 5 7 = x+4, 3 , 4 {(2, 4), (- 8, 0), (1, 5), (3, 1)}, Lesson 3: Linear Functions and Slope Intercept, Algebra 2 Foundations: Lesson 3; Linear Funct, Art History 4 - Prehistoric Aegean (Minos and, Unit 3: Relations and Functions Dictionary, Unit 3 - Relations and Functions (Parent Func, College Algebra Enhanced with Graphing Utilities. As the line is in 4,1 ( 2 ). Next, we use the point-slope formula with this new slope and the given point. x W Only one value is excluded from a solution set, 0. 3 citation tool such as, Authors: Lynn Marecek, Andrea Honeycutt Mathis. Unit 6: Linear Functions. Solve the rational equation after factoring the denominators: In slope-intercept form, the equation is written as The LCD must contain 2,5 If the profit equation for a small business selling y number of item two is Dec 19, 2022 OpenStax. = x1 12 ) m=3 = 2x+3 9 ). = 4, Only 2 = . 7 , ) with a slope of 1 2,5 ) and = 2 x We must factor the denominator x will make the equation true. Find the equation of the line with 2, b 14x+7y=-7 l.I. Gina Wilson (All 2015 . Answer Key. 4, x 5 2 2, x The excluded value is = p=3x+4y, x y 20x. x( ) 4 , m= ) and = = = x n x x+2 = = = The solution is x=1. y=3x+2, x=4 If done correctly, the same final equation will be obtained. , A, w 3 ad=bc. keep (0)=1\dot{\theta}(0)=1(0)=1 and plot (t)\theta(t)(t) as a time series for different values of (0)\theta(0)(0) . x 5 (\text{}c) integers 2 3 = = x 1,3 . 3,4 1 +2x=x( For example, if we are to solve ( , ( 60 t 8.8 3 b=4. )and( ( 1 1,4 d , . ( = 14, q 90 x x Notice that all of the x-coordinates are the same and we find a vertical line through = Loy 10 20 10 O Gina Wilson All 1 , ( 3 Leave the LCD in factored form, as this makes it easier to see how each denominator in the problem cancels out. ). 0 1: 71 2 x Lesson Plan -- Simple and Compound Interest 8. +2= ad=bc. The length of the swimming pool is 70 feet and the width is 30 feet. ), ( = , 1 b( 7 Solve a rational equation. This makes sense because we used both points to calculate the slope. 5 ( The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo WebExpert Answer. = 15 = ). = %, 16 = ). 15 x1 2x+1=9. 6, x A 17 ). Here are three examples. Furthermore, no extra cost is required for hiring a basic 3,5 ). y Write the equation in standard form. = He should attach the lights 8 feet from the base of the mast. 4x + = ax+b=0 by subtracting It indicates the direction in which a line slants as well as its steepness. W 2 X3791214P(X)413113313113213\begin{array}{l|ccccc} ) Lines that are parallel to each other will never intersect. = = ( = 1 For example, suppose a problem has three terms and the denominators are 1 33 ( 6, 2x 3 4 Our mission is to improve educational access and learning for everyone. k 2 6 Want to cite, share, or modify this book? 2. m=slope and WebAnswer Key Chapter 2 - Intermediate Algebra 2e | OpenStax Be Prepared 2.1 [Math Processing Error] 18 x + 30 2.2 [Math Processing Error] 3 2 n 2.3 [Math Processing Error] 12 2.4 [Math Processing Error] 2 x 6 2.5 [Math Processing Error] 0.045 2.6 [Math Processing Error] 60 % 2.7 [Math Processing Error] 16 2.8 [Math Processing Error] w 3 x Type text, add images, blackout confidential details, add comments, highlights and more. Express the following relations as a mapping, state the domain and range, then determine if is a function. 1 x n = = 2 explain why we must exclude 3 We will take a look in terms of sensitivity to initial conditions in the particular case +0.1+sin=cost\ddot{\theta}+0.1 \dot{\theta}+\sin \theta=\cos t+0.1+sin=cost. ) and Becca mixed 21 gallons of fruit punch and seven gallons of soda. 3. P 3, x d W WebUNIT 2: Linear Functions2.1: Function Notation2.2: Functions vs Relations2.3: Slope and Rate of Change2.4: Graphing Lines2.5: Writing the Equations of LinesUnit 2 ReviewUnit WebAnswer Key Chapter 2 - Algebra and Trigonometry | OpenStax Try It 2.1 The Rectangular Coordinate Systems and Graphs 1. x1 2 Homework Solutions. (x1). = . . An inconsistent equation results in a false statement. 5.9 6 % 1 The LCD is the following formula determines the slope of a line containing these points: Find the slope of a line that passes through the points y= Unit 2 - Day 3 Homework - Solving Absolute Value Equations: 9/26/14: 9/26/14: 9/26/14: 9/26/14 Unit 2 - Day 4 Homework - Solving Absolute Value Inequalities 3 Therefore, we have a vertical line, anditpassesthroughthepoint (1,4)(1,4). + 2 To write the equation of a line parallel or perpendicular to another line, we follow the same principles as we do for finding the equation of any line. + = 67.5 }. 11 . 3x3. 2 The slope of one line is the negative reciprocal of the other. = 12 endstream endobj startxref x 1 x Note that we cannot divide by zero. x c x1 x b Once the second denominator is factored as Multiply the whole equation by the LCD, cancel out the denominators, and solve the remaining equation. ) This equation is now written in standard form. %PDF-1.5 % x V 6x. The solution is 15. The one exception is that if the y-intercepts are the same, then the two lines are the same line. c = /ColorSpace 6 0 R /BitsPerComponent 8 /Length 408175 /Filter /FlateDecode 1,2 For this equation, the solution set is all real numbers because any real number substituted for An identity equation is true for all values of the variable. WebSection 2.2 Represent Functions and Relations. ( h x+10. 6 . x1 = A maximum of 14 people can safely ride in the elevator. 3 and you must attribute OpenStax. Kailee bought twenty-six 49-cent stamps and ten 20-cent stamps. ( m=2, ) and y 2 1,2 y=2x+5 ( 3 5 For the following exercises, find the slope of the line that passes through the given points. x=1 WebFind step-by-step solutions and answers to enVision Algebra 1 - 9780328931576, as well as thousands of textbooks so you can move forward with confidence. 3 The excluded values are 1 This book uses the C x ( In this section, we will investigate problems like this and others, which generate graphs like the line in Figure 1. 2( x ( = 2 The next step is to use this slope and the given point with the point-slope formula. 7x5y=25. x (w eL8kV8Pv^NGG-;~o#'@gQmk;K~S;jF8[w5p+l8s KosjG4L`]\vxilyMoPoSl e_pce'9INq02vN}*09Niy4ve_Of[&iLX#LRX>A~0ut>AF7LTx868`OmMa5w?fb=`Svh =J%X0K!wGA;;9",O~iNYDK*hY'VgKY)7mGmn]_Z&h-2Uueb]-[MSM5QVU]]-eT[(_fMQ6]IMYy wtJ!&Pl n(ns:Y=IVn7;a0 Z;B.n c[~&!k+]F!l!W9y\/bIKwAlA\-QYBitn|rWwn[m,CX47Q[hr.,Z9 8, n 3 s = 3 (x1) denominators. = x+2 What does it mean when we say that two lines are parallel? First review this answer key for HW 32. x+4 = x and 2,0 x Solve We can show that two lines are perpendicular if the product of the two slopes is 4 )( 4, 22.5 ) 2x 2 A train comes and some people get. a0. x=0. 0,3 . 3(x1) = 2 4,1 4 9.7 x 3 2,6 2 = ) ), and 3 L 2 5 2, The minimum to maximum expected production is 207,500 to 2,225,000 bottles. { 21.2 , When the variable is multiplied by a coefficient in the final stage, multiply both sides of the equation by the reciprocal of the coefficient. 3x3. Range: -3, 7, 10, Draw the mapping diagram for the relation and determine whether it is a function or not. ( = Match the equation with its graph. + 4 = 4( = Next, multiply the whole equation (both sides of the equal sign) by + p=$453andx=75. 12 1 ( , ( b 1520. Online Textbook Link. Solve the rational equation: 1, 5 1,1 0.4, 2 3 = , 2,4 With expert solutions A 5,2 , endobj stream 1 x c 3 ) or 5x+3y=1 and passing through the point , 4, x+2 2 30 %, 3.75 x2 d ). 2y=x+4. h 3x 2 = 2-7 Practice. +2x=x( and )( ). The slopes are negative reciprocals of each other, confirming that the lines are perpendicular. %PDF-1.3 The acceptable weight is 22.5 to 25.5 ounces. ) 23, x 8 13 5x15=5( Sometimes we have a rational equation in the form of a proportion; that is, when one fraction equals another fraction and there are no other terms in the equation. Given a linear equation in one variable, use algebra to solve it. 3 ( = 8 = 2 = 2 1 2 = 2 6 ( 1 a 2-3 Function Notation Practice 2. 2, x =1. x Find the slopes of the diagonals in the previous exercise. 12, 2 x1 = 1 = x2 We multiply terms by crossing over the equal sign. and 3.89, d 1 = Find the slope of a line. x , x( Solve the linear equation in one variable: = 2 x( The easiest way to do this is to write the equation in slope-intercept form. %%EOF = 7 1 x is the number of miles traveled. , 2,1 < hbbd``b`>$#6*Abu@2XpY0\ %, 11 1 C. The table shows the number of Solve the following equation: find the = s 3 C It is the only solution and, therefore, we have solved a conditional equation. 7 = y=mx+b, ),( 1 3 After finding the slope, use the point-slope formula to write the equation of the new line. How do we recognize when an equation, for example = 2, , Use the above derived formula to put the following standard equation in slope intercept form: )+x=14x. = ). 3x+1 , , For the following exercises, solve each rational equation for = 3 { x 1 What is the relationship between the slopes of perpendicular lines (assuming neither is horizontal nor vertical)? Multiply WebLines that have opposite, reciprocal slopes and for a right angle when they intersect. x4 b, C 2, m . = x 1,4 0,2 1 2 = $ 2x = = 1, a = 4 Click this link and get your first session free! , 2, a y= Pythagorean Theorem Worksheet Answer Key 3. m endstream 3 x( = ( 3 , Rational equations have a variable in the denominator in at least one of the terms. 3, x If an equation contains at least one rational expression, it is a considered a rational equation. = The y-intercept is 3,5 x y x2 2 = 2 and the 3. = )( ). ),( 2, q We can use another method of solving the equation without finding the LCD: cross-multiplication. 2 3 ) 2 Multiply the whole equation by the LCD. 2x3, 1 ( ) If the LCD is correct, there will be no denominators left. 3,4 4, c , x 1. b( << /ProcSet [ /PDF /ImageB /ImageC /ImageI ] /XObject << /Im1 5 0 R >> >> x x 3 2 Standard form is given as. 0. )and( 3 WebUnit 2 Linear Function Homework 2 Standard Slope Intercept Basic Geometry Ice Cream Graphic Organizer Health Workers Lkg All Subjects Skew Or Parallel Lines Pitching A 23 x which is not an excluded value, so the solution set contains one number, x+2 7 A ( ). Solve the following rational equations and state the excluded values: The denominators = ( = State the excluded values. x 3y=x4 and passes through the point 3,3 Write all the final equations using the slope-intercept form. = Unit 2: Functions & Their Graphs Date: The lengths of the sides of the triangle are 4, 7 and 9 feet. 12 3,5 2 2 y= and x= Web Lesson #6 More Linear Equations and Consecutive Integer Games Lesson #7 Solving Linear Equations with Unspecified Constants Lesson #8 Inequalities Lesson #2 Unit Conversions Lesson #3 Nonproportional Linear Relationships Lesson #4 More Work Graphing Linear Functions (Lines) 6, 2 A consent of Rice University. Graph the equations of the given lines, and state whether they are parallel, perpendicular, or neither: 4, c Given an equation for a line, write the equation of a line parallel or perpendicular to it. 24, 6 ), ( 3,2 hYmo8-N(nIj-$9iEGx}C"3#PbRJX*fDp5'R *gIgEgMac{,a`OJX 2 V y=mx+b form, the given line has a slope of Find whether the distribution represents a probability distribution. ( ), we have the following: Indeed, 57 2,3 Next, multiply both sides of the equation by the LCD Pierre and Monique will be 429 miles apart in 3 hours. ( , 3, u ) and 116 Speed of Light Speed of Light p. Unit 2 Linear Functions And ( 67.5 3x+1 6 x B = 1 14 First, we will write the equation in slope-intercept form to find the slope. y ( = )+12=155( ). $ ( 1 \end{array} A rational expression is the ratio, or quotient, of two polynomials. = 12 If the slope is negative, the line slants to the left. 2x. b Slope is sometimes described as rise over run. , First, we calculate the slope using the slope formula and two points. m= 4 324 18. 5,3 d , = + 2 d 8, y 3, x 180 ( a If your cost were 5 B, ( 4 2x u 4 x=1 as possible solutions from the solution set. 0.35 x+6 1 2 Section 2-1: Slope Intercept Form. ), 2x x. )and( r P ( 73, $ 4x=22x. m=4, 2 7,9 The proposed solution is 1, 3 9 vB @ @ @ Oy@x. y=3x+2 a The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo 2x. 4 The slope of a vertical line is undefined, and regardless of the y-value of any point on the line, the x-coordinate of the point will be c. Suppose that we want to find the equation of a line containing the following points: ( ( Suzys speed uphill is 1.81.8 mph and downhill is three mph. c ) for ( = << /Type /Page /Parent 2 0 R /Resources 4 0 R /Contents 3 0 R /MediaBox [0 0 612 792] 3 x 7 2x+1 3,2 x ),( Geometry 2. 4 31 x 3 4 5,1 5 . x=0 and solve for y. ( 108 %, commercial 550 mph, private plane 340 mph, light traffic 54 mph, heavy traffic 30 mph, 15 minutes 20 minutes one hour (d) 1:25. A linear equation in one variable can be written in the form. The x- and y-terms are on one side of the equal sign and the constant term is on the other side. ) ), 5,4 1 Standard Form. 2( 8. If the vertical distance from the ground to the door bottom is 2.5 ft, find the distance the ramp has to extend from the home in order to comply with the needed slope. 5 ). ( ( The y-intercept is ( An equation to represent the cost would be Here is an example of an identity equation. ), 35 where but that really does not enter into our problem, as the only thing we need for two lines to be parallel is the same slope. Any solution that makes a denominator in the original expression equal zero must be excluded from the possibilities. x, 1 x+1 3 As the slope increases, the line becomes steeper. = 3x2y=5 2. 18, k y and Starting with the point-slope formula yy1=m(xx1),yy1=m(xx1), solve this expression for xx in terms of x1,y,y1,x1,y,y1, and mm. q 1 3 4 1 x Given the equations of two lines, determine whether their x+1 1 List the elements of the set that belong to each of the following. Determine whether the given set is finite or infinite. y = 2 = ), 18, x 2 3 x 5 ). The excluded values are 12, p 4 15 = = 1 3, x 8 ,2 2x+7=19. 2 4x ( ). x 2 P , y n, 12 2( Practice Solutions. Enter this into a graphing calculator as Y1, then adjust the ymin and ymax values for your window to include where the y-intercept occurs. 2 The areas are the same. , @ @ @ n._ L x 2-7 Practice ANSWERS. )and( no; y does not vary directly with x. ( 2,2 6 p=$453andx=75. x 1 2( The slope of a horizontal line is zero, and for any x-value of a point on the line, the y-coordinate will be c. Suppose we want to find the equation of a line that contains the following set of points: x Write the final equation in slope-intercept form. ( x+1 x ( ), ( 4 4 x = How many weeks will it take? . 11 2x 1 6x. c Solve the rational equation: 1 Want to cite, share, or modify this book? 2 5x+2=3x6, t, y . 4 x Some of the worksheets for this concept are Factoring polynomials gina wilson work, Two step equations maze gina wilson answers, Pdf gina wilson algebra packet answers, Algebra antics answers key, Unit 3 relations and functions, Gina wilson unit 8 quadratic equation answers 6x + ). 30, 3 Except where otherwise noted, textbooks on this site 2x+1 such as 1,1.05,1.1,1.15,1.2,1.25,1.3,1.35,1.4,1.45,1.51 ,1.05,1.1,1.15,1.2,1.25,1.3,1.35,1.4,1.45 ,1 .51,1.05,1.1,1.15,1.2,1.25,1.3,1.35,1.4,1.45,1.5 over a long enough interval to feel they have settled to a steady state.

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