# 4.2E: Exercises

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$

$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$

( \newcommand{\kernel}{\mathrm{null}\,}\) $$\newcommand{\range}{\mathrm{range}\,}$$

$$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$

$$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$

$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$

$$\newcommand{\Span}{\mathrm{span}}$$

$$\newcommand{\id}{\mathrm{id}}$$

$$\newcommand{\Span}{\mathrm{span}}$$

$$\newcommand{\kernel}{\mathrm{null}\,}$$

$$\newcommand{\range}{\mathrm{range}\,}$$

$$\newcommand{\RealPart}{\mathrm{Re}}$$

$$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$

$$\newcommand{\Argument}{\mathrm{Arg}}$$

$$\newcommand{\norm}[1]{\| #1 \|}$$

$$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$

$$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$

$$\newcommand{\vectorA}[1]{\vec{#1}} % arrow$$

$$\newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow$$

$$\newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vectorC}[1]{\textbf{#1}}$$

$$\newcommand{\vectorD}[1]{\overrightarrow{#1}}$$

$$\newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}}$$

$$\newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}}$$

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$

$$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$

$$\newcommand{\avec}{\mathbf a}$$ $$\newcommand{\bvec}{\mathbf b}$$ $$\newcommand{\cvec}{\mathbf c}$$ $$\newcommand{\dvec}{\mathbf d}$$ $$\newcommand{\dtil}{\widetilde{\mathbf d}}$$ $$\newcommand{\evec}{\mathbf e}$$ $$\newcommand{\fvec}{\mathbf f}$$ $$\newcommand{\nvec}{\mathbf n}$$ $$\newcommand{\pvec}{\mathbf p}$$ $$\newcommand{\qvec}{\mathbf q}$$ $$\newcommand{\svec}{\mathbf s}$$ $$\newcommand{\tvec}{\mathbf t}$$ $$\newcommand{\uvec}{\mathbf u}$$ $$\newcommand{\vvec}{\mathbf v}$$ $$\newcommand{\wvec}{\mathbf w}$$ $$\newcommand{\xvec}{\mathbf x}$$ $$\newcommand{\yvec}{\mathbf y}$$ $$\newcommand{\zvec}{\mathbf z}$$ $$\newcommand{\rvec}{\mathbf r}$$ $$\newcommand{\mvec}{\mathbf m}$$ $$\newcommand{\zerovec}{\mathbf 0}$$ $$\newcommand{\onevec}{\mathbf 1}$$ $$\newcommand{\real}{\mathbb R}$$ $$\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}$$ $$\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}$$ $$\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}$$ $$\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}$$ $$\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$$ $$\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$$ $$\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$$ $$\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$$ $$\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}$$ $$\newcommand{\laspan}[1]{\text{Span}\{#1\}}$$ $$\newcommand{\bcal}{\cal B}$$ $$\newcommand{\ccal}{\cal C}$$ $$\newcommand{\scal}{\cal S}$$ $$\newcommand{\wcal}{\cal W}$$ $$\newcommand{\ecal}{\cal E}$$ $$\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}$$ $$\newcommand{\gray}[1]{\color{gray}{#1}}$$ $$\newcommand{\lgray}[1]{\color{lightgray}{#1}}$$ $$\newcommand{\rank}{\operatorname{rank}}$$ $$\newcommand{\row}{\text{Row}}$$ $$\newcommand{\col}{\text{Col}}$$ $$\renewcommand{\row}{\text{Row}}$$ $$\newcommand{\nul}{\text{Nul}}$$ $$\newcommand{\var}{\text{Var}}$$ $$\newcommand{\corr}{\text{corr}}$$ $$\newcommand{\len}[1]{\left|#1\right|}$$ $$\newcommand{\bbar}{\overline{\bvec}}$$ $$\newcommand{\bhat}{\widehat{\bvec}}$$ $$\newcommand{\bperp}{\bvec^\perp}$$ $$\newcommand{\xhat}{\widehat{\xvec}}$$ $$\newcommand{\vhat}{\widehat{\vvec}}$$ $$\newcommand{\uhat}{\widehat{\uvec}}$$ $$\newcommand{\what}{\widehat{\wvec}}$$ $$\newcommand{\Sighat}{\widehat{\Sigma}}$$ $$\newcommand{\lt}{<}$$ $$\newcommand{\gt}{>}$$ $$\newcommand{\amp}{&}$$ $$\definecolor{fillinmathshade}{gray}{0.9}$$

## Practice Makes Perfect

Recognize the Relationship Between the Solutions of an Equation and its Graph

In the following exercises, for each ordered pair, decide:

1. Is the ordered pair a solution to the equation?
2. Is the point on the line?

y=x+2

1. (0,2)
2. (1,2)
3. (−1,1)
4. (−3,−1)

1. yes; no
2. no; no
3. yes; yes
4. yes; yes

y=x−4

1. (0,−4)
2. (3,−1)
3. (2,2)
4. (1,−5)

### Exercise $$\PageIndex{3}$$

$$y=\frac{1}{2} x-3$$

1. (0,−3)
2. (2,−2)
3. (−2,−4)
4. (4,1)

1. yes; yes
2. yes; yes
3. yes; yes
4. no; no

### Exercise $$\PageIndex{4}$$

$$y=\frac{1}{3} x+2$$

1. (0,2)
2. (3,3)
3. (−3,2)
4. (−6,0)

Graph a Linear Equation by Plotting Points

In the following exercises, graph by plotting points.

### Exercise $$\PageIndex{5}$$

$$y=3 x-1$$

### Exercise $$\PageIndex{6}$$

$$y=2 x+3$$

### Exercise $$\PageIndex{7}$$

$$y=-2 x+2$$

### Exercise $$\PageIndex{8}$$

$$y=-3 x+1$$

### Exercise $$\PageIndex{9}$$

$$y=x+2$$

### Exercise $$\PageIndex{10}$$

$$y=x-3$$

### Exercise $$\PageIndex{11}$$

$$y=-x-3$$

### Exercise $$\PageIndex{12}$$

$$y=-x-2$$

### Exercise $$\PageIndex{13}$$

$$y=2 x$$

### Exercise $$\PageIndex{14}$$

$$y=3 x$$

### Exercise $$\PageIndex{15}$$

$$y=-4 x$$

### Exercise $$\PageIndex{16}$$

$$y=-2 x$$

### Exercise $$\PageIndex{17}$$

$$y=\frac{1}{2} x+2$$

### Exercise $$\PageIndex{18}$$

$$y=\frac{1}{3} x-1$$

### Exercise $$\PageIndex{19}$$

$$y=\frac{4}{3} x-5$$

### Exercise $$\PageIndex{20}$$

$$y=\frac{3}{2} x-3$$

### Exercise $$\PageIndex{21}$$

$$y=-\frac{2}{5} x+1$$

### Exercise $$\PageIndex{22}$$

$$y=-\frac{4}{5} x-1$$

### Exercise $$\PageIndex{23}$$

$$y=-\frac{3}{2} x+2$$

### Exercise $$\PageIndex{24}$$

$$y=-\frac{5}{3} x+4$$

### Exercise $$\PageIndex{25}$$

$$x+y=6$$

### Exercise $$\PageIndex{26}$$

$$x+y=4$$

### Exercise $$\PageIndex{27}$$

$$x+y=-3$$

### Exercise $$\PageIndex{28}$$

$$x+y=-2$$

### Exercise $$\PageIndex{29}$$

$$x-y=2$$

### Exercise $$\PageIndex{30}$$

$$x-y=1$$

### Exercise $$\PageIndex{31}$$

$$x-y=-1$$

### Exercise $$\PageIndex{32}$$

$$x-y=-3$$

### Exercise $$\PageIndex{33}$$

$$3 x+y=7$$

### Exercise $$\PageIndex{34}$$

$$5x+y=6$$

2x+y=−3

### Exercise $$\PageIndex{36}$$

$$4x+y=−5$$

### Exercise $$\PageIndex{37}$$

$$\frac{1}{3} x+y=2$$

### Exercise $$\PageIndex{38}$$

$$\frac{1}{2} x+y=3$$

### Exercise $$\PageIndex{39}$$

$$\frac{2}{5} x-y=4$$

### Exercise $$\PageIndex{40}$$

$$\frac{3}{4} x-y=6$$

### Exercise $$\PageIndex{41}$$

$$2 x+3 y=12$$

4x+2y=12

3x−4y=12

2x−5y=10

x−6y=3

x−4y=2

5x+2y=4

### Exercise $$\PageIndex{48}$$

3x+5y=5

Graph Vertical and Horizontal Lines

In the following exercises, graph each equation.

x=4

x=3

x=−2

x=−5

y=3

y=1

y=−5

y=−2

### Exercise $$\PageIndex{57}$$

$$x=\frac{7}{3}$$

### Exercise $$\PageIndex{58}$$

$$x=\frac{5}{4}$$

### Exercise $$\PageIndex{59}$$

$$y=-\frac{15}{4}$$

### Exercise $$\PageIndex{60}$$

$$y=-\frac{5}{3}$$

In the following exercises, graph each pair of equations in the same rectangular coordinate system.

y=2x and y=2

y=5x and y=5

### Exercise $$\PageIndex{63}$$

$$y=-\frac{1}{2} x$$ and $$y=-\frac{1}{2}$$

### Exercise $$\PageIndex{64}$$

$$y=-\frac{1}{3} x$$ and $$y=-\frac{1}{3}$$

## Mixed Practice

In the following exercises, graph each equation.

y=4x

y=2x

### Exercise $$\PageIndex{67}$$

$$y=-\frac{1}{2} x+3$$

### Exercise $$\PageIndex{68}$$

$$y=\frac{1}{4} x-2$$

y=−x

y=x

x−y=3

x+y=−5

4x+y=2

2x+y=6

y=−1

y=5

2x+6y=12

5x+2y=10

x=3

x=−4

## Everyday Math

### Exercise $$\PageIndex{81}$$

Motor home cost. The Robinsons rented a motor home for one week to go on vacation. It cost them $594 plus$0.32 per mile to rent the motor home, so the linear equation y=594+0.32x gives the cost, yy, for driving xx miles. Calculate the rental cost for driving 400, 800, and 1200 miles, and then graph the line.

## Writing Exercises

### Exercise $$\PageIndex{83}$$

Explain how you would choose three $$x$$ - values to make a table to graph the line $$y=\frac{1}{5} x-2$$

### Exercise $$\PageIndex{84}$$

What is the difference between the equations of a vertical and a horizontal line?

## Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

ⓑ After reviewing this checklist, what will you do to become confident for all goals?

This page titled 4.2E: Exercises is shared under a not declared license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.