1.2E: Exercises - Solving Linear Equations in Two Variables
- Page ID
- 147253
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)PROBLEM SET: GRAPHING A LINEAR EQUATION
Work the following problems.
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1) Is the point (2, 3) on the line 5x - 2y = 4? |
2) Is the point (1, - 2) on the line 6x - y = 4? |
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3) For the line 3x - y = 12, complete the following ordered pairs. (2,___) (___, 6) (0,___) (___, 0) |
4) For the line 4x + 3y = 24, complete the following ordered pairs. (3,___) (___, 4) (0,___) (___, 0) |
Graph the following equations using intercepts.
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5) Graph 2x + 4 = 0 |
6) Graph 2y - 6 = 0 |
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7) Graph the following three equations on the same set of coordinate axes. \[y = x +1 \quad y = 2x + 1 \quad y = -x + 1 \nonumber \] |
8) Graph the following three equations on the same set of coordinate axes. \[y = 2x +1 \quad y = 2x \quad y = 2x - 1 \nonumber \] |
Find the slope of the line passing through the following pair of points.
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9) (2, 3) and (5, 9) |
10) (4, 1) and (2, 5) |
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11) (- 1, 1) and (1, 3) |
12) (4, 3) and (- 1, 3) |
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13) (3, 4) and (3, 7) |
14) (- 2, 4) and (- 3, - 2) |
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15) (- 3, - 5) and (- 1, - 7) |
16) (0, 4) and (3, 0) |
Determine the slope of the line from the given equation of the line.
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17) y = - 2x + 1 |
18) y = 3x - 2 |
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19) 2x - y = 6 |
20) x + 3y = 6 |
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21) 3x - 4y = 12 |
22) What is the slope of the x-axis? |
Graph the line that passes through the given point and has the given slope.
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23) (1, 2) and m = - 3/4 |
24) (2, - 1) and m = 2/3 |
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25) (0, 2) and m = - 2 |
26) (2, 3) and m = 0 |
Graph the following equations using their slope and y-intercept.
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27) Graph y = 2x + 3 |
28) Graph y = - 3x + 5 |
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29) Graph y = 4x - 3 |
30) Graph x - 2y = 8 |
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31) Graph 2x + y = 4 |
32) Graph 2x - 3y = 6 |