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



��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. �



��slope: , y-intercept: 3


� 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. �



��slope: , y-intercept: í2


� 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



��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



��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.



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





��(í3, í1), slope



��(5, í2), slope



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



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)



��(í4, 3), (1, 13)




��(3, 5), (5, 6)



��(3, 5), (5, 6)




��(2, 4), (7, 2)



��(2, 4), (7, 2)




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



��&$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. �


� 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



��(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)

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��y + 4 = (x í 3)

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��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)

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



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.�



��(í5, í2), y = x + 4

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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



��(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

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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



��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.



� Write the equation in slope-intercept form for the line of fit. �

6$/(�



��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�



��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.



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)}.



��

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



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



��f (x) = 3x + 8

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�

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

��

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�

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

��

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



��

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

��

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



study guide and review %2d chapter 4

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