Section 1
Linear Equations in Two Variables
Fill in each blank with the correct response.The point with coordinates (0,0) is the ______ of a rectangular coordinate system.
Fill in each blank with the correct response.For any value of $x,$ the point $(x, 0)$ lies on the ___________ axis. For any value of $y,$ the point $(0, y)$ lies on the-axis.
Fill in each blank with the correct response.To find the $x$ -intercept of a line, we let ___________ equal 0 and solve for To find the$y$ -intercept, we let __________ equal 0 and solve for _____________
Fill in each blank with the correct response.The equation $y=4$ has a ___________ line as its graph, and $x=4$ has a ____________ line as its graph.
Fill in each blank with the correct response.To graph a straight line, we must find a minimum of $\longrightarrow$ points. The points $(3,$ and $(\longrightarrow, 4)$ lie on the graph of $2 x-3 y=0$.
Fill in each blank with the correct response.The equation of the $x$ -axis is ______________. The equation of the $y$ -axis is _______________
Solve each problem by locating ordered pairs on the graphs.The graph indicates personal spending in billions of dollars on medical care in the United States.Data from Centers for Medicare \& Medicaid Services.(a) If $(x, y)$ represents a point on the graph, what does $x$ represent? What does $y$ represent?(b) Estimate spending in 2016 .(c) Write an ordered pair $(x, y)$ that represents approximate spending in 2016 .(d) In what year was spending about $\$ 2200$ billion?
Solve each problem by locating ordered pairs on the graphs.The graph shows the percentage of Americans who moved in selected years.(a) If the ordered pair $(x, y)$ represents a point on the graph, what does $x$ represent? What does $y$ represent?(b) Estimate the percentage of Americans who moved in 2017 .(c) Write an ordered pair $(x, y)$ that gives the approximate percentage of Americans who moved in 2017 .(d) What does the ordered pair ( 1960,20 ) mean in the context of this graph?
Name the quadrant, if any, in which each point is located. See Objective $2 .$(a) (1,6)(b) (-4,-2)(c) (-3,6)(d) (7,-5)(e) (-3,0)(f) (0,-0.5)
Name the quadrant, if any, in which each point is located. See Objective $2 .$(a) (-2,-10)(b) (4,8)(c) (-9,12)(d) (3,-9)(e) (0,-8)(f) (2.5,0)
Use the given information to determine the quadrants in which the point $(x, y)$ must lie. (Hint: Consider the signs of the coordinates in each quadrant, and the signs of their product and quotient.)(a) $x y>0$(b) $x y<0$(c) $\frac{x}{y}<0$(d) $\frac{x}{y}>0$
What must be true about the value of at least one of the coordinates of any point that lies along an axis?
A student plotted the point with coordinates (-4,2) incorrectly by moving 2 units from 0 to the right along the $x$ -axis and then 4 units down parallel to the $y$ -axis. WHAT WENT WRONG?
A student incorrectly claimed that the point (0,-4) lies on the $x$ -axis because the $x$ -coordinate is $0 .$ WHAT WENT WRONG?
Plot each point in a rectangular coordinate system. See Objective $2 .$(2,3)
Plot each point in a rectangular coordinate system. See Objective $2 .$(-1,2)
Plot each point in a rectangular coordinate system. See Objective $2 .$(-3,-2)
Plot each point in a rectangular coordinate system. See Objective $2 .$(1,-4)
Plot each point in a rectangular coordinate system. See Objective $2 .$(0,5)
Plot each point in a rectangular coordinate system. See Objective $2 .$(-2,-4)
Plot each point in a rectangular coordinate system. See Objective $2 .$(-2,4)
Plot each point in a rectangular coordinate system. See Objective $2 .$(3,0)
Plot each point in a rectangular coordinate system. See Objective $2 .$(-2,0)
Plot each point in a rectangular coordinate system. See Objective $2 .$(3,-3)
Complete the given table for each equation and then graph the equation.$$\begin{aligned}&y=x-4\\&\begin{array}{c|c}x & y \\\hline 0 & \\\hline 1 & \\\hline 2 & \\\hline 3 & \\\hline 4 & \\\hline\end{array}\end{aligned}$$
Complete the given table for each equation and then graph the equation.$$\begin{aligned}&y=x+3\\&\begin{array}{c|c}x & y \\\hline 0 & \\\hline 1 & \\\hline 2 & \\\hline 3 & \\\hline 4 &\end{array}\end{aligned}$$
Complete the given table for each equation and then graph the equation.$$\begin{array}{c|c}x-y=3 \\x & y \\\hline 0 & \\\hline & 0 \\\hline 5 & \\\hline 2 &\end{array}$$
Complete the given table for each equation and then graph the equation.$$\begin{aligned}&x-y=\\&x-y\\&\begin{array}{c|c}x & y \\\hline 0 & \\\hline & 0 \\\hline 1 & \\\hline 3 &\end{array}\end{aligned}$$
Complete the given table for each equation and then graph the equation.$$\begin{aligned}&x+2 y=5\\&\begin{array}{c|c}x & y \\\hline 0 & \\\hline & 0 \\\hline 2 & \\\hline & 2 \\\hline\end{array}\end{aligned}$$
Complete the given table for each equation and then graph the equation.$$\begin{aligned}&x+3 y=-5\\&\begin{array}{c|c}x & y \\\hline 0 & \\\hline & 0 \\\hline 1 & \\\hline & -1\end{array}\end{aligned}$$
Complete the given table for each equation and then graph the equation.$$\begin{aligned}&4 x-5 y=20\\&\begin{array}{c|c}x & y \\\hline 0 & \\\hline & 0 \\\hline 2 & \\\hline & -3 \\\hline\end{array}\end{aligned}$$
Complete the given table for each equation and then graph the equation.$$\begin{aligned}&6 x-5 y=30\\&\begin{array}{c|c}x & y \\\hline 0 & \\\hline & 0 \\\hline 3 & \\\hline & -2\end{array}\end{aligned}$$
Match each equation in parts (a)-(d) with its graph in choices A-D. (Coordinates of the points shown are integers.)(a) $x+3 y=3$(b) $x-3 y=-3$(c) $x-3 y=3$(d) $x+3 y=-3$
Which of the following equations have a graph that is a horizontal line? A vertical line?A. $x-6=0$B. $x+y=0$C. $y+3=0$D. $y=-10$E. $x+1=5$
Find the $x$ - and y-intercepts. Then graph each equation. See Examples $2-4 .$35. $2 x+3 y=12$
Find the $x$ - and y-intercepts. Then graph each equation. See Examples $2-4 .$36. $5 x+2 y=10$
Find the $x$ - and y-intercepts. Then graph each equation. See Examples $2-4 .$37. $x-3 y=6$
Find the $x$ - and y-intercepts. Then graph each equation. See Examples $2-4 .$38. $x-2 y=-4$
Find the $x$ - and y-intercepts. Then graph each equation. See Examples $2-4 .$5 x+6 y=-10
Find the $x$ - and y-intercepts. Then graph each equation. See Examples $2-4 .$3 x-7 y=9
Find the $x$ - and y-intercepts. Then graph each equation. See Examples $2-4 .$$\frac{2}{3} x-3 y=7$
Find the $x$ - and y-intercepts. Then graph each equation. See Examples $2-4 .$$\frac{5}{7} x+\frac{6}{7} y=-2$
Find the $x$ - and y-intercepts. Then graph each equation. See Examples $2-4 .$$x+5 y=0$
Linear Equations, Graphs, and Functions$x-3 y=0$
Linear Equations, Graphs, and Functions$2 x+y=0$
Linear Equations, Graphs, and Functions$4 x-y=0$
Linear Equations, Graphs, and Functions$2 x=3 y$
Linear Equations, Graphs, and Functions$4 y=3 x$
Linear Equations, Graphs, and Functions$-\frac{2}{3} y=x$
Linear Equations, Graphs, and Functions$-\frac{3}{4} y=x$
Linear Equations, Graphs, and Functions$y=5$
Linear Equations, Graphs, and Functions$y=-3$
Linear Equations, Graphs, and Functions$x=2$
Linear Equations, Graphs, and Functions$x=-3$
Linear Equations, Graphs, and Functions$x+4=0$
Linear Equations, Graphs, and Functions$x-4=0$
Linear Equations, Graphs, and Functions$y+2=0$
Linear Equations, Graphs, and Functions$y-5=0$
Each table of values gives several points that lie on a line.(a) What is the $x$ -intercept of the line? The y-intercept?(b) Which equation in choices $A-D$ corresponds to the given table of values?(c) Graph the equation.$$\begin{array}{|r|r|}\hline x & y \\\hline-4 & -3 \\\hline-2 & 0 \\\hline 0 & 3 \\\hline 2 & 6\end{array}$$A. $3 x+2 y=6$B. $3 x-2 y=-6$C. $3 x+2 y=-6$D. $3 x-2 y=6$
Each table of values gives several points that lie on a line.(a) What is the $x$ -intercept of the line? The y-intercept?(b) Which equation in choices $A-D$ corresponds to the given table of values?(c) Graph the equation.$$\begin{array}{|c|c}\hline x & y \\\hline-1 & 6 \\\hline 0 & 4 \\\hline 1 & 2 \\\hline 2 & 0 \\\hline\end{array}$$A. $2 x-y=4$B. $2 x+y=-4$C. $2 x+y=4$D. $2 x-y=-4$
Each table of values gives several points that lie on a line.(a) What is the $x$ -intercept of the line? The y-intercept?(b) Which equation in choices $A-D$ corresponds to the given table of values?(c) Graph the equation.$$\begin{array}{|c|c|}\hline x & y \\\hline-2 & -1 \\\hline 0 & -1 \\\hline 2 & -1 \\\hline 4 & -1\end{array}$$A. $y=-1$B. $y=1$C. $x=1$D. $x=-1$
Each table of values gives several points that lie on a line.(a) What is the $x$ -intercept of the line? The y-intercept?(b) Which equation in choices $A-D$ corresponds to the given table of values?(c) Graph the equation.$$\begin{array}{r|r}x & y \\\hline 6 & -1 \\\hline 6 & 0 \\\hline 6 & 1 \\\hline 6 & 2\end{array}$$A. $x=-6$B. $y=0$C. $y=6$D. $x=6$
Find the midpoint of each segment with the given endpoints. See Example 5(-8,4) and (-2,-6)
Find the midpoint of each segment with the given endpoints. See Example 5(5,2) and (-1,8)
Find the midpoint of each segment with the given endpoints. See Example 5(3,-6) and (6,3)
Find the midpoint of each segment with the given endpoints. See Example 5(-10,4) and (7,1)
Find the midpoint of each segment with the given endpoints. See Example 5(-9,3) and (9,8)
Find the midpoint of each segment with the given endpoints. See Example 5(4,-3) and (-1,3)
Find the midpoint of each segment with the given endpoints. See Example 5(2.5,3.1) and (1.7,-1.3)
Find the midpoint of each segment with the given endpoints. See Example 5(6.2,5.8) and (1.4,-0.6)
Find the midpoint of each segment with the given endpoints.$\left(\frac{1}{2}, \frac{1}{3}\right)$ and $\left(\frac{3}{2}, \frac{5}{3}\right)$
Find the midpoint of each segment with the given endpoints.$\left(\frac{21}{4}, \frac{2}{5}\right)$ and $\left(\frac{7}{4}, \frac{3}{5}\right)$
Find the midpoint of each segment with the given endpoints.$\left(-\frac{1}{3}, \frac{2}{7}\right)$ and $\left(-\frac{1}{2}, \frac{1}{14}\right)$
Find the midpoint of each segment with the given endpoints.$\left(\frac{3}{5},-\frac{1}{3}\right)$ and $\left(\frac{1}{2},-\frac{7}{2}\right)$
Segment $P Q$ has the given coordinates for one endpoint $P$ and for its midpoint $M$. Find the coordinates of the other endpoint $Q .$ (Hint: Represent $Q$ by $(x, y)$ and write two equations using the midpoint formula, one involving $x$ and the other involving $y .$ Then solve for $x$ and $y .)$$P(5,8), M(8,2)$
Segment $P Q$ has the given coordinates for one endpoint $P$ and for its midpoint $M$. Find the coordinates of the other endpoint $Q .$ (Hint: Represent $Q$ by $(x, y)$ and write two equations using the midpoint formula, one involving $x$ and the other involving $y .$ Then solve for $x$ and $y .)$$P(7,10), M(5,3)$
Segment $P Q$ has the given coordinates for one endpoint $P$ and for its midpoint $M$. Find the coordinates of the other endpoint $Q .$ (Hint: Represent $Q$ by $(x, y)$ and write two equations using the midpoint formula, one involving $x$ and the other involving $y .$ Then solve for $x$ and $y .)$$P(1.5,1.25), M(3,1)$
Segment $P Q$ has the given coordinates for one endpoint $P$ and for its midpoint $M$. Find the coordinates of the other endpoint $Q .$ (Hint: Represent $Q$ by $(x, y)$ and write two equations using the midpoint formula, one involving $x$ and the other involving $y .$ Then solve for $x$ and $y .)$$P(2.5,1.75), M(3,2)$