study guide and review %2d chapter 4

State whether each sentence is true or false . If false , replace the underlined term to make a true sentence.

���The y-intercept is the y-coordinate of the point where the graph crosses the y-axis.

62/87,21���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 is called linear regression.

62/87,21���The statement is false. The process of using a linear equation to make predictions about values that are beyond the range of the data is called linear extrapolation. Linear regression is an algorithm to find a precise line of fit for a set RI�GDWD��

���An inverse relation is the set of ordered pairs obtained by exchanging the x-coordinates with the y-coordinates of each ordered pair of a relation.

62/87,21���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 how closely the regression equation is modeling the data.

62/87,21���The correlation coefficient describes whether the correlation between the variables is positive or negative and how closely the equation is modeling the data. So, the statement is true.

���Lines in the same plane that do not intersect are called parallel lines.

62/87,21���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.

62/87,21���The statement is false. Lines that intersect at right angles are called perpendicular lines. Acute angles have PHDVXUHV�OHVV�WKDQ�����

���A(n) constant function can generate ordered pairs for an inverse relation.

62/87,21���A constant function has the same function value for every element of the domain. An inverse function can generate RUGHUHG�SDLUV�IRU�DQ�LQYHUVH�UHODWLRQ��6R��WKH�VWDWHPHQW�LV�IDOVH��5HSODFH�FRQVWDQW�IXQFWLRQ�ZLWK�LQYHUVH�IXQFWLRQ�WR�make it a true statement.

���The range of a relation is the range of its inverse function.

62/87,21���7KH�UDQJH�RI�D�UHODWLRQ�LV�WKH�GRPDLQ�RI�WKH�LQYHUVH�RI�WKH�UHODWLRQ��7KH�VWDWHPHQW�LV�IDOVH��

���An equation of the form y = mx + b is in point-slope form.

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Study Guide and Review - Chapter 4

���An equation of the form y = mx + b is in point-slope form.

62/87,21���An equation in point slope form looks like y ± y1 = m(x í�x1). 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 the equation.

����slope: 3, y-intercept: 5

62/87,21���The 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 line through the two points.

y

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Study Guide and Review - Chapter 4

����slope:í2, y-intercept: í9

62/87,21���The 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, í9). Then move down 2 units and right 1 unit. Plot the point. Draw a line through the two points. �

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Study Guide and Review - Chapter 4

����slope: , y-intercept: 3

62/87,21���The 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 line through the two points. �

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Study Guide and Review - Chapter 4

����slope: , y-intercept: í2

62/87,21���The 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, í2). Then move down 5 units and right 8 units. Plot the point. Draw a line through the two points. �

Graph each equation.����y = 4x í 2

62/87,21���To graph the equation, plot the y-intercept (0, í2). Then move up 4 units and right 1 unit. Plot the point. Draw a line through the two points.

y x

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Study Guide and Review - Chapter 4

����y = í3x + 5

62/87,21���To 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.

�����

62/87,21���To graph the equation, plot the y-intercept (0, 1). Then move up 1 unit and right 2 units. Plot the point. Draw a line through the two points.

����3x + 4y = 8

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Study Guide and Review - Chapter 4

����3x + 4y = 8

62/87,21���First, 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 line through the two points.

����6.,�5(17$/��Write an equation in slope-intercept form for the total cost of skiing for h hours with one lift ticket.

62/87,21���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.

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Study Guide and Review - Chapter 4

Write an equation of the line that passes through the given point and has the given slope.����(1, 2), slope 3

62/87,21���Find the y-intercept. �

� Write the equation in slope-intercept form.�

����(2, í6), slope í4

62/87,21���Find the y-intercept. �

� Write the equation in slope-intercept form.�

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Study Guide and Review - Chapter 4

����(í3, í1), slope

62/87,21���Find the y-intercept. �

� Write the equation in slope-intercept form.�

����(5, í2), slope

62/87,21���Find the y-intercept. �

� Write the equation in slope-intercept form.�

Write an equation of the line that passes through the given points.

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Study Guide and Review - Chapter 4

Write an equation of the line that passes through the given points.����(2, í1), (5, 2)

62/87,21���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. �

����(í4, 3), (1, 13)

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Study Guide and Review - Chapter 4

����(í4, 3), (1, 13)

62/87,21���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)

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Study Guide and Review - Chapter 4

����(3, 5), (5, 6)

62/87,21���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)

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Study Guide and Review - Chapter 4

����(2, 4), (7, 2)

62/87,21���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. �

����&$03��In 2005, a camp had 450 campers. Five years later, the number of campers rose to 750. Write a linear

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Study Guide and Review - Chapter 4

����&$03��In 2005, a camp had 450 campers. Five years later, the number of campers rose to 750. Write a linear equation that represents the number of campers that attend camp.

62/87,21���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 slope provided.

����(6, 3), slope 5

62/87,21���

����(í2, 1), slope í3

62/87,21���

����(í4, 2), slope 0

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Study Guide and Review - Chapter 4

����(í4, 2), slope 0

62/87,21���

Write each equation in standard form.����y í 3 = 5(x í 2)

62/87,21���

����y í 7 = í3(x + 1)

62/87,21���

����y + 4 = (x í 3)

62/87,21���

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Study Guide and Review - Chapter 4

����y í 9 = (x + 2)

62/87,21���

Write each equation in slope-intercept form.����y í 2 = 3(x í 5)

62/87,21���

����y í 12 = í2(x í 3)

62/87,21���

����y + 3 = 5(x + 1)

62/87,21���

����y í 4 = (x + 2)

62/87,21���

Write an equation in slope-intercept form for the line that passes through the given point and is parallel

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Study Guide and Review - Chapter 4

Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the graph of each equation.

����(2, 5), y = x í 3

62/87,21���The slope of the line with equation y = x í 3 is 1. The line parallel to y = x í 3 has the same slope, 1.�

����(0, 3), y = 3x + 5

62/87,21���The slope of the line with equation y = 3x + 5 is 3. The line parallel to y = 3x + 5 has the same slope, 3.�

����(í4, 1), y = í2x í 6

62/87,21���The slope of the line with equation y = í2x í 6 is í2. The line parallel to y = í2x í 6 has the same slope, í2.�

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Study Guide and Review - Chapter 4

����(í5, í2), y = x + 4

62/87,21���

The 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 is perpendicular to the graph of the given equation.

����(2, 4), y = 3x + 1

62/87,21���The slope of the line with equation y = 3x + 1 is 3. The slope of the perpendicular line is the opposite reciprocal of 3,

or í .

�

y x

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Study Guide and Review - Chapter 4

����(1, 3), y = í2x í 4

62/87,21���The slope of the line with equation y = í2x í 4 is í2. The slope of the perpendicular line is the opposite reciprocal of

í2, or .

�

����(í5, 2), y = x + 4

62/87,21���

The slope of the line with equation y = x + 4 is . The slope of the perpendicular line is the opposite reciprocal of

, or í3.

�

����(3, 0), y = x

62/87,21���

The slope of the line with equation y = x is . The slope of the perpendicular line is the opposite reciprocal of

, or 2.

�

����Determine whether the graph shows a positive , a negative, or no correlation. If there is a positive or negative

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Study Guide and Review - Chapter 4

����Determine whether the graph shows a positive , a negative, or no correlation. If there is a positive or negative correlation, describe its meaning.

62/87,21���The graph shows a positive correlation. As the number of hours spent studying increases, the test scores increase.

����$77(1'$1&(� A scatter plot of data compares the number of years since a business has opened and its annual number of sales. It contains the ordered pairs (2, 650) and (5, 1280). Write an equation in slope-intercept form for the line of fit for this situation.

62/87,21���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. �

6$/(�

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Study Guide and Review - Chapter 4

����6$/(� The table shows the number of purchases made at an outerwear store during a sale. Write an equation of the regression line. Then estimate the number of sales on day 10 of the sale. �

�

62/87,21���Use a calculator to find the equation of the regression line. �

� y = 5.36x + 11 � To 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.

029,(6�

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Study Guide and Review - Chapter 4

����029,(6� The table shows ticket sales at a certain theater during the first week after a movie opened. Write an equation of the regression line. Then estimate the daily ticket sales on the 15th day. �

�

62/87,21���Use a calculator to find the equation of the regression line. �

� y = í5.79x + 99.14 � To 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.

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Study Guide and Review - Chapter 4

Find the inverse of each relation.����{(7, 3.5), (6.2, 8), (±4, 2.7), (±12, 1.4)}

62/87,21���To find the inverse, exchange the coordinates of the ordered pairs.� ���������ĺ��������� � (6.2, 8) ĺ��������� � (±��������ĺ�������±4) � (±12, 1.4) ĺ�������±12) � The inverse is {(3.5, 7), (8, 6.2), (2.7, �4), (1.4, ����`�����

����{(1, 9), (13, 26), (±3, 4), (±11, ±2)}

62/87,21���To find the inverse, exchange the coordinates of the ordered pairs.� �������ĺ������� � ���������ĺ��������� � (±������ĺ�����±3) � (±11, ±���ĺ��±2, ±11) � The inverse is {(9, 1), (26, 13), (4, �3), (�2, �11)}.

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Study Guide and Review - Chapter 4

����

62/87,21���To find the inverse, exchange the coordinates of the ordered pairs.� (±��������ĺ�������±4) � (±��������ĺ�������±1) � ���������ĺ��������� � ���������ĺ��������� � The inverse is {(2.7, �4), (3.8, �����������������������`��

����

62/87,21���To find the inverse, exchange the coordinates of the ordered pairs.� (±�������ĺ�����±12) � (±������ĺ�����±8) � (±4, ±���ĺ��±4, ±4) � (0, ±���ĺ��±8, 0) � The inverse is {(4, �12), (0, �8), (�4, �4), (�8, 0)}.

Find the inverse of each function

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Study Guide and Review - Chapter 4

Find the inverse of each function

����

62/87,21���

� Write the final equation in slope-intercept form. So, f -1(x) = .

����f (x) = 3x + 8

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Study Guide and Review - Chapter 4

����f (x) = 3x + 8

62/87,21���

�

Write the final equation in slope-intercept form. So, .

����

62/87,21���

�

Write the final equation in slope-intercept form. So, .

����

62/87,21���

� Write the final equation in slope-intercept form. So, f -1(x) = 4x + 28.

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Study Guide and Review - Chapter 4

����

62/87,21���

� Write the final equation in slope-intercept form. So, .

����

62/87,21���

� Write the final equation in slope-intercept form. So, .

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Study Guide and Review - Chapter 4