Study Guide and Review %2D Chapter 4
Transcript of 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.
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���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
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����(í2, 1), slope í3
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����(í4, 2), slope 0
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Study Guide and Review - Chapter 4
����(í4, 2), slope 0
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Write each equation in standard form.����y í 3 = 5(x í 2)
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����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)
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Write each equation in slope-intercept form.����y í 2 = 3(x í 5)
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����y í 12 = í2(x í 3)
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����y + 3 = 5(x + 1)
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����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
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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
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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