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Section 1

Use the Rectangular Coordinate System

In the following exercises, plot each point in a rectangular coordinate system and identify the quadrant in which the point is located. (a) (-4,2)(b) (-1,-2)(c) (3,-5)(d) (-3,5)(e) $\left(\frac{5}{3}, 2\right)$

In the following exercises, plot each point in a rectangular coordinate system and identify the quadrant in which the point is located. (a) (-2,-3)(b) (3,-3)c) (-4,1)(d) (4,-1)(e) $\left(\frac{3}{2}, 1\right)$

In the following exercises, plot each point in a rectangular coordinate system and identify the quadrant in which the point is located. (a) (3,-1)(b) (-3,1)(c) (-2,2)(1) (-4,-3)(e) $\left(1, \frac{14}{5}\right)$

In the following exercises, plot each point in a rectangular coordinate system and identify the quadrant in which the point is located. (a) (-1,1)(b) (-2,-1)(c) (2,1)(d) (1,-4)(e) $\left(3, \frac{7}{2}\right)$

In the following exercises, plot each point in a rectangular coordinate system. (a) (-2,0)(b) (-3,0)(c) (0,0)(e) (0,4)(c) (0,2)

In the following exercises, plot each point in a rectangular coordinate system. (a) (0,1)(b) (0,-4)(c) (-1,0)(d) (0,0)(e) (5,0)

In the following exercises, plot each point in a rectangular coordinate system. (a) (0,0)(b) (0,-3)(c) (-4,0)(d) (1,0)e) (0,-2)

In the following exercises, plot each point in a rectangular coordinate system. (a) (-3,0)(b) (0,5)(c) (0,-2)(d) (2,0)(e) (0,0)

In the following exercises, name the ordered pair of each point shown in the rectangular coordinate system.

In the following exercises, which ordered pairs are solutions to the given equations? $2 x+y=6$(a) (1,4)(B) (3,0)(c) (2,3)

In the following exercises, which ordered pairs are solutions to the given equations? $x+3 y=9$(a) (0,3)(b) (6,1)(c) (-3,-3)

In the following exercises, which ordered pairs are solutions to the given equations? $4 x-2 y=8$(a) (3,2)(b) (1,4)(c) (0,-4)

In the following exercises, which ordered pairs are solutions to the given equations? $3 x-2 y=12$(a) (4,0)(b) (2,-3)c) (1,6)

In the following exercises, which ordered pairs are solutions to the given equations? $y=4 x+3$(a) (4,3)(b) (-1,-1)(c) $\left(\frac{1}{2}, 5\right)$

In the following exercises, which ordered pairs are solutions to the given equations? $y=2 x-5$(a) (0,-5)(b) (2,1)(c) $\left(\frac{1}{2},-4\right)$

In the following exercises, which ordered pairs are solutions to the given equations? $y=\frac{1}{2} x-1$(a) (2,0)(b) (-6,-4)(c) (-4,-1)

In the following exercises, which ordered pairs are solutions to the given equations? $y=\frac{1}{3} x+1$(a) (-3,0)(b) (9,4)c) (-6,-1)

In the following exercises, complete the table to find solutions to each linear equation. $y=2 x-4$$$\begin{array}{|c|c|c|}\hline \boldsymbol{x} & \boldsymbol{y} & (\boldsymbol{x}, \boldsymbol{y}) \\\hline 0 & & \\\hline 2 & & \\\hline-1 & & \\\hline\end{array}$$

In the following exercises, complete the table to find solutions to each linear equation. $y=3 x-1$$$\begin{array}{|c|c|c|}\hline \boldsymbol{x} & \boldsymbol{y} & (\boldsymbol{x}, \boldsymbol{y}) \\\hline 0 & & \\\hline 2 & & \\\hline-1 & & \\\hline\end{array}$$

In the following exercises, complete the table to find solutions to each linear equation. y=-x+5$$\begin{array}{|c|c|c|}\hline \boldsymbol{x} & \boldsymbol{y} & (\boldsymbol{x}, \boldsymbol{y}) \\\hline 0 & & \\\hline -3 & & \\\hline2 & & \\\hline\end{array}$$

In the following exercises, complete the table to find solutions to each linear equation. $y=-x+2$$$\begin{array}{|c|c|c|}\hline \boldsymbol{x} & \boldsymbol{y} & (\boldsymbol{x}, \boldsymbol{y}) \\\hline 0 & & \\\hline -3 & & \\\hline2 & & \\\hline\end{array}$$

In the following exercises, complete the table to find solutions to each linear equation. $y=\frac{1}{3} x+1$$$\begin{array}{|c|c|c|}\hline \boldsymbol{x} & \boldsymbol{y} & (\boldsymbol{x}, \boldsymbol{y}) \\\hline 0 & & \\\hline 3 & & \\\hline6& & \\\hline\end{array}$$

In the following exercises, complete the table to find solutions to each linear equation. $y=\frac{1}{2} x+4$$$\begin{array}{|c|c|c|}\hline \boldsymbol{x} & \boldsymbol{y} & (\boldsymbol{x}, \boldsymbol{y}) \\\hline 0 & & \\\hline 2 & & \\\hline4& & \\\hline\end{array}$$

In the following exercises, complete the table to find solutions to each linear equation. $y=-\frac{3}{2} x-2$$$\begin{array}{|c|c|c|}\hline \boldsymbol{x} & \boldsymbol{y} & (\boldsymbol{x}, \boldsymbol{y}) \\\hline 0 & & \\\hline 2 & & \\\hline-2& & \\\hline\end{array}$$

In the following exercises, complete the table to find solutions to each linear equation. $y=-\frac{3}{2} x-2$$$\begin{array}{|c|c|c|}\hline \boldsymbol{x} & \boldsymbol{y} & (\boldsymbol{x}, \boldsymbol{y}) \\\hline 0 & & \\\hline 3 & & \\\hline-3& & \\\hline\end{array}$$

In the following exercises, complete the table to find solutions to each linear equation. $x+3 y=6$$$\begin{array}{|c|c|c|}\hline \boldsymbol{x} & \boldsymbol{y} & (\boldsymbol{x}, \boldsymbol{y}) \\\hline 0 & & \\\hline 3 & & \\\hline0& & \\\hline\end{array}$$

In the following exercises, complete the table to find solutions to each linear equation. $x+2 y=8$$$\begin{array}{|c|c|c|}\hline \boldsymbol{x} & \boldsymbol{y} & (\boldsymbol{x}, \boldsymbol{y}) \\\hline 0 & & \\\hline 4 & & \\\hline0& & \\\hline\end{array}$$

In the following exercises, complete the table to find solutions to each linear equation. $2 x-5 y=10$$$\begin{array}{|c|c|c|}\hline \boldsymbol{x} & \boldsymbol{y} & (\boldsymbol{x}, \boldsymbol{y}) \\\hline 0 & & \\\hline 10 & & \\\hline0& & \\\hline\end{array}$$

In the following exercises, complete the table to find solutions to each linear equation. $3 x-4 y=12$$$\begin{array}{|c|c|c|}\hline \boldsymbol{x} & \boldsymbol{y} & (\boldsymbol{x}, \boldsymbol{y}) \\\hline 0 & & \\\hline 8 & & \\\hline0& & \\\hline\end{array}$$

In the following exercises, find three solutions to each linear equation.$y=5 x-8$

In the following exercises, find three solutions to each linear equation.$y=3 x-9$

In the following exercises, find three solutions to each linear equation.$y=-4 x+5$

In the following exercises, find three solutions to each linear equation.$y=-2 x+7$

In the following exercises, find three solutions to each linear equation.$x+y=8$

In the following exercises, find three solutions to each linear equation.$x+y=6$

In the following exercises, find three solutions to each linear equation. $x+y=-2$

In the following exercises, find three solutions to each linear equation.$x+y=-1$

In the following exercises, find three solutions to each linear equation.$3 x+y=5$

In the following exercises, find three solutions to each linear equation. $2 x+y=3$

In the following exercises, find three solutions to each linear equation. $4 x-y=8$

In the following exercises, find three solutions to each linear equation.$5 x-y=10$

In the following exercises, find three solutions to each linear equation. $2 x+4 y=8$

In the following exercises, find three solutions to each linear equation.$3 x+2 y=6$

In the following exercises, find three solutions to each linear equation.$5 x-2 y=10$

In the following exercises, find three solutions to each linear equation.$4 x-3 y=12$

Weight of a baby. Mackenzie recorded her baby's weight every two months. The baby's age, in months, and weight, in pounds, are listed in the table below, and shown as an ordered pair in the third column.(a) Plot the points on a coordinate plane.(b) Why is only Quadrant I needed?

Latresha recorded her son's height and weight every year. His height, in inches, and weight, in pounds, are listed in the table below, and shown as an ordered pair in the third column.(a) Plot the points on a coordinate plane.(b) Why is only Quadrant I needed?

Explain in words how you plot the point (4,-2) in

How do you determine if an ordered pair is aa rectangular coordinate system. solution to a given equation?

Is the point (-3,0) on the $x$ -axis or $y$ -axis? How do

Is the point (0,8) on the $x$ -axis or $y$ -axis? How do you know? $\quad$ you know?

In the following exercises, for each ordered pair, decide: (a) Is the ordered pair a solution to the equation?(b) Is the point on the line? $y=x+2$(a) (0,2)(b) (1,2)(c) (-1,1)(d) (-3,-1)

In the following exercises, for each ordered pair, decide: (a) Is the ordered pair a solution to the equation?(b) Is the point on the line?$y=x-4$(a) (0,-4)(b) (3,-1)(c) (2,2)(d) (1,-5)

In the following exercises, for each ordered pair, decide: (a) Is the ordered pair a solution to the equation?(b) Is the point on the line?$y=\frac{1}{2} x-3$(a) (0,-3)(b) (2,-2)(c) (-2,-4)(d) (4,1)

In the following exercises, for each ordered pair, decide: (a) Is the ordered pair a solution to the equation?(b) Is the point on the line?$y=\frac{1}{3} x+2$(a) (0,2)(b) (3,3)(c) (-3,2)(d) (-6,0)