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Section 1
Graphing Equations
Plot each point and name the quadrant or axis in which the point lies. See Example 1.$$(3,2)$$
Plot each point and name the quadrant or axis in which the point lies. See Example 1.$$(2,-1)$$
Plot each point and name the quadrant or axis in which the point lies. See Example 1.$$(-5,3)$$
Plot each point and name the quadrant or axis in which the point lies. See Example 1.$$(-3,-1)$$
Plot each point and name the quadrant or axis in which the point lies. See Example 1.$$\left(5 \frac{1}{2}-4\right)$$
Plot each point and name the quadrant or axis in which the point lies. See Example 1.$$\left(-2,6 \frac{1}{3}\right)$$
Plot each point and name the quadrant or axis in which the point lies. See Example 1.$$(0,3,5)$$
Plot each point and name the quadrant or axis in which the point lies. See Example 1.$$(-52,0)$$
Plot each point and name the quadrant or axis in which the point lies. See Example 1.$$(-2,-4)$$
Plot each point and name the quadrant or axis in which the point lies. See Example 1.$$(-42,0)$$
Determine the coordinates of each point on the graph See Example $\boldsymbol{l}$.Point $C$
Determine the coordinates of each point on the graph See Example $\boldsymbol{l}$.Point $D$
Determine the coordinates of each point on the graph See Example $\boldsymbol{l}$.Point $E$
Determine the coordinates of each point on the graph See Example $\boldsymbol{l}$.Point $F$
Determine the coordinates of each point on the graph See Example $\boldsymbol{l}$.Point $A$
Determine the coordinates of each point on the graph See Example $\boldsymbol{l}$.Point $B$
Determine whether each ordered pair is a solution of the given equation. See Example 2.$$y=3 x-5 \text { i }(0,5),(-1,-8)$$
Determine whether each ordered pair is a solution of the given equation. See Example 2.$$y=-2 x+7 ;(1,5),(-2,3)$$
Determine whether each ordered pair is a solution of the given equation. See Example 2.$$-6 x+5 y=-6 ;(1,0),\left(2, \frac{6}{5}\right)$$
Determine whether each ordered pair is a solution of the given equation. See Example 2.$$y=2 x^{2}-(1,2) \cdot(3,18)$$
Determine whether each ordered pair is a solution of the given equation. See Example 2.$$y=2|x|:(-1,2),(0,2)$$
Determine whether each ordered pair is a solution of the given equation. See Example 2 .$y=x^{3} ;(2,8),(3,9)$
Determine whether each ordered pair is a solution of the given equation. See Example 2.$$y=x^{4}+(-1,1),(2,16)$$
Determine whether each ordered pair is a solution of the given equation. See Example 2.$$y=\sqrt{x}+2 ;(1,3),(4,4)$$
Determine whether each ordered pair is a solution of the given equation. See Example 2.$$y=\sqrt[3]{x}-4 ;(1,-3),(8,6)$$
Determine whether each equation is linear or not. Then graph the equation by finding and plotting ordered pair solutions. See Examples 3 through 7.$$x+y=3$$
Determine whether each equation is linear or not. Then graph the equation by finding and plotting ordered pair solutions. See Examples 3 through 7.$$y-x=8$$
Determine whether each equation is linear or not. Then graph the equation by finding and plotting ordered pair solutions. See Examples 3 through 7.$$y=4 x$$
Determine whether each equation is linear or not. Then graph the equation by finding and plotting ordered pair solutions. See Examples 3 through 7.$$y=6 x$$
Determine whether each equation is linear or not. Then graph the equation by finding and plotting ordered pair solutions. See Examples 3 through 7.$$y=4 x-2$$
Determine whether each equation is linear or not. Then graph the equation by finding and plotting ordered pair solutions. See Examples 3 through 7.$$y=6 x-5$$
Determine whether each equation is linear or not. Then graph the equation by finding and plotting ordered pair solutions. See Examples 3 through 7.$$y=|x|+3$$
Determine whether each equation is linear or not. Then graph the equation by finding and plotting ordered pair solutions. See Examples 3 through 7.$$y=|x|+2$$
Determine whether each equation is linear or not. Then graph the equation by finding and plotting ordered pair solutions. See Examples 3 through 7.$$2 x-y=5$$
Determine whether each equation is linear or not. Then graph the equation by finding and plotting ordered pair solutions. See Examples 3 through 7.$$4 x-y=7$$
Determine whether each equation is linear or not. Then graph the equation by finding and plotting ordered pair solutions. See Examples 3 through 7.$$y=2 x^{2}$$
Determine whether each equation is linear or not. Then graph the equation by finding and plotting ordered pair solutions. See Examples 3 through 7.$$y=3 x^{2}$$
Determine whether each equation is linear or not. Then graph the equation by finding and plotting ordered pair solutions. See Examples 3 through 7.$$y=x^{2}-3$$
Determine whether each equation is linear or not. Then graph the equation by finding and plotting ordered pair solutions. See Examples 3 through 7.$$y=x^{2}+3$$
Determine whether each equation is linear or not. Then graph the equation by finding and plotting ordered pair solutions. See Examples 3 through 7.$$y=-2 x$$
Determine whether each equation is linear or not. Then graph the equation by finding and plotting ordered pair solutions. See Examples 3 through 7.$$y=-3 x$$
Determine whether each equation is linear or not. Then graph the equation by finding and plotting ordered pair solutions. See Examples 3 through 7.$$y=-2 x+3$$
Determine whether each equation is linear or not. Then graph the equation by finding and plotting ordered pair solutions. See Examples 3 through 7.$$y=-3 x+2$$
Determine whether each equation is linear or not. Then graph the equation by finding and plotting ordered pair solutions. See Examples 3 through 7.$$y=|x+2|$$
Determine whether each equation is linear or not. Then graph the equation by finding and plotting ordered pair solutions. See Examples 3 through 7.$$y=|x-1|$$
Determine whether each equation is linear or not. Then graph the equation by finding and plotting ordered pair solutions. See Examples 3 through 7.$$y=x^{3}$$
Determine whether each equation is linear or not. Then graph the equation by finding and plotting ordered pair solutions. See Examples 3 through 7.$$\begin{aligned}&y=x^{3}-2\\&\text { (Hint. Let }x=-3,-2,-1,0,1,2 .)\end{aligned}$$
Determine whether each equation is linear or not. Then graph the equation by finding and plotting ordered pair solutions. See Examples 3 through 7.$$y=-|x|$$
Determine whether each equation is linear or not. Then graph the equation by finding and plotting ordered pair solutions. See Examples 3 through 7.$$y=-x^{2}$$
Determine whether each equation is linear or not. Then graph the equation by finding and plotting ordered pair solutions. See Examples 3 through 7.$$y=\frac{1}{3} x-1$$
Determine whether each equation is linear or not. Then graph the equation by finding and plotting ordered pair solutions. See Examples 3 through 7.$$y=\frac{1}{2} x-3$$
Determine whether each equation is linear or not. Then graph the equation by finding and plotting ordered pair solutions. See Examples 3 through 7.$$y=-\frac{3}{2} x+1$$
Determine whether each equation is linear or not. Then graph the equation by finding and plotting ordered pair solutions. See Examples 3 through 7.$$y=-\frac{2}{3} x+1$$
Solve the following equations. See Section 2.1.$$3(x-2)+5 x=6 x-16$$
Solve the following equations. See Section 2.1.$$5+7(x+1)=12+10 x$$
Solve the following equations. See Section 2.1.$$3 x+\frac{2}{5}=\frac{1}{10}$$
Solve the following equations. See Section 2.1.$$\frac{1}{6}+2 x=\frac{2}{3}$$
Solve the following inequalities. See Section 2.4.$$3 x \leq-15$$
Solve the following inequalities. See Section 2.4.$$-3 x>18$$
Solve the following inequalities. See Section 2.4.$$2 x-5>4 x+3$$
Solve the following inequalities. See Section 2.4.$$9 x+8 \leq 6 x-4$$
Without graphing, visualize the location of each point. Then give its location by quadrant or $x$ - or $y$ -axis.$$(4,-2)$$
Without graphing, visualize the location of each point. Then give its location by quadrant or $x$ - or $y$ -axis.$$(-42,17)$$
Without graphing, visualize the location of each point. Then give its location by quadrant or $x$ - or $y$ -axis.$$(0,-100)$$
$$(-87,0)$$
Without graphing, visualize the location of each point. Then give its location by quadrant or $x$ - or $$(-10,-30)$$
Without graphing, visualize the location of each point. Then give its location by quadrant or $x$ - or $$(0,0)$$
Given that $x$ is a positive number and that $y$ is a positive number, determine the quadrant or axis in which each point lies.$$(x,-y)$$
Given that $x$ is a positive number and that $y$ is a positive number, determine the quadrant or axis in which each point lies.$$(-x, y)$$
Given that $x$ is a positive number and that $y$ is a positive number, determine the quadrant or axis in which each point lies.$$(x, 0)$$
Given that $x$ is a positive number and that $y$ is a positive number, determine the quadrant or axis in which each point lies.$$(0,-y)$$
Given that $x$ is a positive number and that $y$ is a positive number, determine the quadrant or axis in which each point lies.$$(-x,-y)$$
Given that $x$ is a positive number and that $y$ is a positive number, determine the quadrant or axis in which each point lies.$$(0,0)$$
Solve. See the Concept Check in this section.Which correctly describes the location of the point $(-1,5.3)$ in a rectangular coordinate system?a. 1 unit to the right of the $y$ -axis and 5.3 units above the $x$ -axisb. 1 unit to the left of the $y$ -axis and 5.3 units above the $x$ -axisc. 1 unit to the left of the $y$ -axis and 5.3 units below the $x$ -axisd. 1 unit to the right of the $y$ -axis and 5.3 units below the $x$ -axis
Solve. See the Concept Check in this section.Which correctly describes the location of the point $\left(0,-\frac{3}{4}\right)$ in a rectangular coordinate system?a. on the $x$ -axis and $\frac{3}{4}$ unit to the left of the $y$ -axisb. on the $x$ -axis and $\frac{3}{4}$ unit to the right of the $y$ -axisc. on the $y$ -axis and $\frac{3}{4}$ unit above the $x$ -axisd. on the $y$ -axis and $\frac{3}{4}$ unit below the $x$ -axiss
Match each description with the graph that best illustrates it.Moe worked 40 hours per week until the fall semester started. He quit and didn’t work again until he worked 60 hours a week during the holiday season starting mid-December.
Match each description with the graph that best illustrates it.Kawana worked 40 hours a week for her father during the summer. She slowly cut back her hours to not working at all during the fall semester. During the holiday season in December, she started working again and increased her hours to 60 hours per week.
Match each description with the graph that best illustrates it.Wendy worked from July through February, never quitting. She worked between 10 and 30 hours per week.
Bartholomew worked from July through February. During the holiday season between mid-November and the beginning of January, he worked 40 hours per week. The rest ofthe time, he worked between 10 and 40 hours per week.a. GRAPH CAN'T COPY!b. GRAPH CAN'T COPY!c. GRAPH CAN'T COPY!d. GRAPH CAN'T COPY!
This broken-line graph shows the hourly minimum wage and the years it increased. Use this graph for Exercises 81 through 84.What was the first year that the minimum hourly wage rose above $\$ 5.00 ?$
This broken-line graph shows the hourly minimum wage and the years it increased. Use this graph for Exercises 81 through 84.What was the first year that the minimum hourly wage rose above $\$ 6.00 ?$
This broken-line graph shows the hourly minimum wage and the years it increased. Use this graph for Exercises 81 through 84.Why do you think that this graph is shaped the way it is?
This broken-line graph shows the hourly minimum wage and the years it increased. Use this graph for Exercises 81 through 84.The federal hourly minimum wage started in 1938 at $\$ 0.25$ How much will it have increased by $2011 ?$
This broken-line graph shows the hourly minimum wage and the years it increased. Use this graph for Exercises 81 through 84.Graph $y=x^{2}-4 x+7 .$ Let $x=0,1,2,3,4$ to generate ordered pair solutions.
This broken-line graph shows the hourly minimum wage and the years it increased. Use this graph for Exercises 81 through 84.Graph $y=x^{2}+2 x+3 .$ Let $x=-3,-2,-1,0,1$ to generate ordered pair solutions.
This broken-line graph shows the hourly minimum wage and the years it increased. Use this graph for Exercises 81 through 84.The perimeter $y$ of a rectangle whose width is a constant 3 inches and whose length is $x$ inches is given by the equation$$y=2 x+6$$a. Draw a graph of this equation.b. Read from the graph the perimeter $y$ of a rectangle whose length $x$ is 4 inches.IMAGE CAN'T COPY!
This broken-line graph shows the hourly minimum wage and the years it increased. Use this graph for Exercises 81 through 84.The distance $y$ traveled in a train moving at a constant speed of 50 miles per hour is given by the equation$$y=50 x$$where $x$ is the time in hours traveled.a. Draw a graph of this equation.b. Read from the graph the distance $y$ traveled after 6 hours.
For income tax purposes, the owner of Copy Services uses a method called straight-line depreciation to show the loss in value of a copy machine he recently purchased. He assumes that he can use the machine for 7 years. The following graph shows the valueof the machine over the years. Use this graph to answer Exercises89 through 94.What was the purchase price of the copy machine?
For income tax purposes, the owner of Copy Services uses a method called straight-line depreciation to show the loss in value of a copy machine he recently purchased. He assumes that he can use the machine for 7 years. The following graph shows the valueof the machine over the years. Use this graph to answer Exercises89 through 94.What is the depreciated value of the machine in 7 years?
For income tax purposes, the owner of Copy Services uses a method called straight-line depreciation to show the loss in value of a copy machine he recently purchased. He assumes that he can use the machine for 7 years. The following graph shows the valueof the machine over the years. Use this graph to answer Exercises89 through 94.What loss in value occurred during the first year?
For income tax purposes, the owner of Copy Services uses a method called straight-line depreciation to show the loss in value of a copy machine he recently purchased. He assumes that he can use the machine for 7 years. The following graph shows the valueof the machine over the years. Use this graph to answer Exercises89 through 94.What loss in value occurred during the second year?
For income tax purposes, the owner of Copy Services uses a method called straight-line depreciation to show the loss in value of a copy machine he recently purchased. He assumes that he can use the machine for 7 years. The following graph shows the valueof the machine over the years. Use this graph to answer Exercises89 through 94.Why do you think that this method of depreciating is called straight-line depreciation?
For income tax purposes, the owner of Copy Services uses a method called straight-line depreciation to show the loss in value of a copy machine he recently purchased. He assumes that he can use the machine for 7 years. The following graph shows the valueof the machine over the years. Use this graph to answer Exercises89 through 94.Why is the line tilted downward?
For income tax purposes, the owner of Copy Services uses a method called straight-line depreciation to show the loss in value of a copy machine he recently purchased. He assumes that he can use the machine for 7 years. The following graph shows the valueof the machine over the years. Use this graph to answer Exercises89 through 94.On the same set of axes, graph $y=2 x, y=2 x-5,$ and $y=2 x+5 .$ What patterns do you see in these graphs?
For income tax purposes, the owner of Copy Services uses a method called straight-line depreciation to show the loss in value of a copy machine he recently purchased. He assumes that he can use the machine for 7 years. The following graph shows the valueof the machine over the years. Use this graph to answer Exercises89 through 94.On the same set of axes, graph $y=2 x, y=x,$ and $y=-2 x$ Describe the differences and similarities in these graphs.
Write each statement as an equation in two variables. Then graph each equation.The $y$ -value is 5 more than three times the $x$ -value.
Write each statement as an equation in two variables. Then graph each equation.The $y$ -value is $-3$ decreased by twice the $x$ -value.
Write each statement as an equation in two variables. Then graph each equation.The $y$ -value is 2 more than the square of the $x$ -value.
Write each statement as an equation in two variables. Then graph each equation.The $y$ -value is 5 decreased by the square of the $x$ -value.
Use a graphing calculator to verify the graphs of the following exercises.Exercise 39
Use a graphing calculator to verify the graphs of the following exercises.Exercise 40
Use a graphing calculator to verify the graphs of the following exercises.Exercise 47
Use a graphing calculator to verify the graphs of the following exercises.Exercise 48
