Study Guide And Review %2D Chapter 4

Study Guide and Review - Chapter 4State whether each sentence is true or false . If false , replace the underlined term to make a truesentence.The y-intercept is the y-coordinate of the point where the graph crosses the y-axis.The y-intercept is the point where the graph crosses the y-axis. So, the statement is true.The process of using a linear equation to make predictions about values that are beyond the range of the data iscalled linear regression.The statement is false. The process of using a linear equation to make predictions about values that are beyond therange of the data is called linear extrapolation. Linear regression is an algorithm to find a precise line of fit for a setAn inverse relation is the set of ordered pairs obtained by exchanging the x-coordinates with the y-coordinates ofeach ordered pair of a relation.This is the definition of an inverse function.Therefore, the statement is true.The correlation coefficient describes whether the correlation between the variables is positive or negative and howclosely the regression equation is modeling the data.The correlation coefficient describes whether the correlation between the variables is positive or negative and howclosely the equation is modeling the data. So, the statement is true.Lines in the same plane that do not intersect are called parallel lines.Lines in the same plane that do not intersect are called parallel lines. So, the statement is true.Lines that intersect at acute angles are called perpendicular lines.The statement is false. Lines that intersect at right angles are called perpendicular lines. Acute angles haveA(n) constant function can generate ordered pairs for an inverse relation.A constant function has the same function value for every element of the domain. An inverse function can generatemake it a true statement.The range of a relation is the range of its inverse function.An equation of the form y mx b is in point-slope form.eSolutions Manual - Powered by CogneroPage 1

Study Guide and Review - Chapter 4An equation of the form y mx b is in point-slope form.An equation in point slope form looks like yy 1 m(xx1). An equation in slope intercept form looks like y mx b. The statement is false.Write an equation of a line in slope-intercept form with the given slope and y-intercept. Then graph theequation.slope: 3, y-intercept: 5The slope-intercept form of a line is y mx b, where m is the slope, and b is the y-intercept.To graph the equation, plot the y-intercept (0, 5). Then move down 3 units and left 1 unit. Plot the point. Draw a linethrough the two points.yeSolutions Manual - Powered by CogneroPage 2

Study Guide and Review - Chapter 4slope: 2, y-intercept: 9The slope-intercept form of a line is y mx b, where m is the slope, and b is the y -intercept.To graph the equation, plot the y-intercept (0, 9). Then move down 2 units and right 1 unit. Plot the point. Draw aline through the two points.eSolutions Manual - Powered by CogneroPage 3

Study Guide and Review - Chapter 4slope:, y-intercept: 3The slope-intercept form of a line is y mx b, where m is the slope, and b is the y -intercept.To graph the equation, plot the y-intercept (0, 3). Then move up 2 units and right 3 units. Plot the point. Draw a linethrough the two points.eSolutions Manual - Powered by CogneroPage 4

Study Guide and Review - Chapter 4slope:, y-intercept: 2The slope-intercept form of a line is y mx b, where m is the slope, and b is the y -intercept.To graph the equation, plot the y-intercept (0, 2). Then move down 5 units and right 8 units. Plot the point. Draw aline through the two points.Graph each equation.y 4x 2To graph the equation, plot the y-intercept (0, 2). Then move up 4 units and right 1 unit. Plot the point. Draw a linethrough the two points.yxeSolutions Manual - Powered by CogneroPage 5

Study Guide and Review - Chapter 4y 3x 5To graph the equation, plot the y-intercept (0, 5). Then move down 3 units and right 1 unit. Plot the point. Draw a linethrough the two points.To graph the equation, plot the y-intercept (0, 1). Then move up 1 unit and right 2 units. Plot the point. Draw a linethrough the two points.3x 4y 8eSolutions Manual - Powered by CogneroPage 6

Study Guide and Review - Chapter 43x 4y 8First, rewrite the equation in slope-intercept form by solving for y.To graph the equation, plot the y-intercept (0, 2). Then down 3 units and right 4 units. Plot the point. Draw a linethrough the two points.Write an equation in slope-intercept form for the total cost of skiing for h hours with one lift ticket.The rate of 5 per hour represents the rate or slope. The cost of the lift ticket is a constant 15, no matter how manyhours you ski. So, the total cost of skiing for h hours can be written as y 5h 15.Write an equation of the line that passes through the given point and has the given slope.eSolutions Manual - Powered by CogneroPage 7

Study Guide and Review - Chapter 4Write an equation of the line that passes through the given point and has the given slope.(1, 2), slope 3Find the y-intercept.Write the equation in slope-intercept form.(2, 6), slope 4Find the y-intercept.Write the equation in slope-intercept form.eSolutions Manual - Powered by CogneroPage 8

Study Guide and Review - Chapter 4( 3, 1), slopeFind the y-intercept.Write the equation in slope-intercept form.(5, 2), slopeFind the y-intercept.Write the equation in slope-intercept form.Write an equation of the line that passes through the given points.eSolutions Manual - Powered by CogneroPage 9

Study Guide and Review - Chapter 4Write an equation of the line that passes through the given points.(2, 1), (5, 2)Find the slope of the line containing the given points.Use the slope and either of the two points to find the y-intercept.Write the equation in slope-intercept form.( 4, 3), (1, 13)eSolutions Manual - Powered by CogneroPage 10

Study Guide and Review - Chapter 4( 4, 3), (1, 13)Find the slope of the line containing the given points.Use the slope and either of the two points to find the y-intercept.Write the equation in slope-intercept form.(3, 5), (5, 6)eSolutions Manual - Powered by CogneroPage 11

Study Guide and Review - Chapter 4(3, 5), (5, 6)Find the slope of the line containing the given points.Use the slope and either of the two points to find the y-intercept.Write the equation in slope-intercept form.(2, 4), (7, 2)eSolutions Manual - Powered by CogneroPage 12

Study Guide and Review - Chapter 4(2, 4), (7, 2)Find the slope of the line containing the given points.Use the slope and either of the two points to find the y-intercept.Write the equation in slope-intercept form.In 2005, a camp had 450 campers. Five years later, the number of campers rose to 750. Write a lineareSolutions Manual - Powered by CogneroPage 13

Study Guide and Review - Chapter 4In 2005, a camp had 450 campers. Five years later, the number of campers rose to 750. Write a linearequation that represents the number of campers that attend camp.Let x be the number of years since 2005. Two points on the line are (0, 450) and (5, 750). Find the slope of the line.Use the slope and either of the two points to find the y-intercept.Write the equation in slope-intercept form.The number of campers that attend camp can be represented by the linear equation y 60x 450.Write an equation in point-slope form for the line that passes through the given point with the slopeprovided.(6, 3), slope 5( 2, 1), slope 3( 4, 2), slope 0eSolutions Manual - Powered by CogneroPage 14

Study Guide and Review - Chapter 4( 4, 2), slope 0Write each equation in standard form.y 3 5(x 2)y7 3(x 1)y 4 (x3)eSolutions Manual - Powered by CogneroPage 15

Study Guide and Review - Chapter 4y9 (x 2)Write each equation in slope-intercept form.y 2 3(x 5)y12 2(x3)y 3 5(x 1)y4 (x 2)Write an equation in slope-intercept form for the line that passes through the given point and is paralleleSolutions Manual - Powered by CogneroPage 16

Study Guide and Review - Chapter 4Write an equation in slope-intercept form for the line that passes through the given point and is parallelto the graph of each equation.(2, 5), y x 3The slope of the line with equation y x3 is 1. The line parallel to y x3 has the same slope, 1.(0, 3), y 3x 5The slope of the line with equation y 3x 5 is 3. The line parallel to y 3x 5 has the same slope, 3.( 4, 1), y 2x6The slope of the line with equation y 2xeSolutions Manual - Powered by Cognero6 is 2. The line parallel to y 2x6 has the same slope, 2.Page 17

Study Guide and Review - Chapter 4( 5, 2), y x 4The slope of the line with equation y x 4 is. The line parallel to y x 4 has the same slope,.Write an equation in slope-intercept form for the line that passes through the given point and isperpendicular to the graph of the given equation.(2, 4), y 3x 1The slope of the line with equation y 3x 1 is 3. The slope of the perpendicular line is the opposite reciprocal of 3,or.yxeSolutions Manual - Powered by CogneroPage 18

Study Guide and Review - Chapter 4(1, 3), y 2x4The slope of the line with equation y 2x2, or4 is 2. The slope of the perpendicular line is the opposite reciprocal of.( 5, 2), y x 4The slope of the line with equation y x 4 is. The slope of the perpendicular line is the opposite reciprocal ofx is. The slope of the perpendicular line is the opposite reciprocal of, or 3.(3, 0), y xThe slope of the line with equation y , or 2.Determine whether the graph shows a positive , a negative, or no correlation. If there is a positive or negativeeSolutions Manual - Powered by CogneroPage 19

Study Guide and Review - Chapter 4Determine whether the graph shows a positive , a negative, or no correlation. If there is a positive or negativecorrelation, describe its meaning.The graph shows a positive correlation. As the number of hours spent studying increases, the test scores increase.A scatter plot of data compares the number of years since a business has opened and its annualnumber of sales. It contains the ordered pairs (2, 650) and (5, 1280). Write an equation in slope-intercept form forthe line of fit for this situation.Find the slope of the line containing the given points.Use the slope and either of the two points to find the y-intercept.Write the equation in slope-intercept form for the line of fit.eSolutions Manual - Powered by CogneroPage 20

Study Guide and Review - Chapter 4The table shows the number of purchases made at an outerwear store during a sale. Write an equation ofthe regression line. Then estimate the number of sales on day 10 of the sale.Use a calculator to find the equation of the regression line.y 5.36x 11To estimate the number of sales on day 10 of the sale, evaluate the regression equation for x 10.The number of sales on day 10 of the sale should be about 65.eSolutions Manual - Powered by CogneroPage 21

Study Guide and Review - Chapter 4The table shows ticket sales at a certain theater during the first week after a movie opened. Write anequation of the regression line. Then estimate the daily ticket sales on the 15th day.Use a calculator to find the equation of the regression line.y 5.79x 99.14To estimate the daily ticket sales on the 15th day, evaluate the regression equation for x 15.The daily ticket sales on the 15th day after a movie opens is 12.29.Find the inverse of each relation.eSolutions Manual - Powered by CogneroPage 22

Study Guide and Review - Chapter 4Find the inverse of each relation.{(7, 3.5), (6.2, 8), ( 4, 2.7), ( 12, 1.4)}To find the inverse, exchange the coordinates of the ordered pairs.(6.2, 8)(4)( 12, 1.4)12)The inverse is {(3.5, 7), (8, 6.2), (2.7, 4), (1.4,{(1, 9), (13, 26), ( 3, 4), ( 11, 2)}To find the inverse, exchange the coordinates of the ordered pairs.(3)( 11,2, 11)The inverse is {(9, 1), (26, 13), (4, 3), ( 2, 11)}.eSolutions Manual - Powered by CogneroPage 23