Masharti muhimu Sura ya 04: Grafu
- Page ID
- 177817
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- Mstari wa mipaka
- Mstari na equation\(Ax+By=C\) ambayo hutenganisha kanda ambapo\(Ax+By>C\) kutoka kanda ambapo\(Ax+By<C\).
- Geoboard
- Geoboard ni bodi yenye gridi ya magogo juu yake.
- Grafu ya Equation ya Mstari
- Grafu ya equation ya mstari\(Ax+By=C\) ni mstari wa moja kwa moja. Kila hatua kwenye mstari ni suluhisho la equation. Kila ufumbuzi wa equation hii ni hatua juu ya mstari huu.
- Mstari wa usawa
- Mstari wa usawa ni grafu ya equation ya fomu\(y=b\). Mstari unapita kupitia y -axis saa\((0,b)\).
- Intercepts ya Line
- Pointi ambapo mstari unavuka\(x\) -axis na\(y\) -axis huitwa intercepts ya mstari.
- Mlinganyo wa mstari
- Equation linear ni ya fomu\(Ax+By=C\), wapi\(A\) na\(B\) si wote sifuri, inaitwa equation linear katika vigezo mbili.
- Ukosefu wa usawa wa mstari
- Ukosefu wa usawa ambao unaweza kuandikwa katika mojawapo ya fomu zifuatazo:
\[Ax+By>C \qquad Ax+By≥C \qquad Ax+By<C \qquad Ax+By≤C\]
wapi\(A\) na\(B\) si wote sifuri.
- Mteremko hasi
- Mteremko mbaya wa mstari unashuka unaposoma kutoka kushoto kwenda kulia.
- kuamuru jozi
- Jozi iliyoamriwa\((x,y)\) inatoa kuratibu ya uhakika katika mfumo wa kuratibu mstatili.
- Mwanzo
- Hatua\((0,0)\) inaitwa asili. Ni hatua ambapo\(x\) -axis na\(y\) -axis intersect.
- Mistari Sambamba
- Mistari katika ndege moja ambayo haipatikani.
- Perpendicular mistari
- Mistari katika ndege moja ambayo huunda angle sahihi.
- Point—Fomu ya mteremko
- Aina ya hatua-mteremko wa equation ya mstari na mteremko\(m\) na iliyo na uhakika\((x_1,y_1)\) ni\(y−y_1=m(x−x_1)\).
- Chanya mteremko
- Mteremko mzuri wa mstari unaendelea unaposoma kutoka kushoto kwenda kulia.
- Quadrant
- \(x\)Mhimili na -axis\(y\) hugawanya ndege katika mikoa minne, inayoitwa quadrants.
- Mfumo wa Kuratibu mstatili
- Mfumo wa gridi hutumika katika algebra kuonyesha uhusiano kati ya vigezo viwili; pia huitwa\(xy\) -plane au 'kuratibu plane'.
- Rise
- Kuongezeka kwa mstari ni mabadiliko yake ya wima.
- Kukimbia
- Kukimbia kwa mstari ni mabadiliko yake ya usawa.
- mteremko formula
- Mteremko wa mstari kati ya pointi mbili\((x_1,y_1)\) na\((x_2,y_2)\) ni\(m=\frac{y_2−y_1}{x_2−x_1}\).
- Mteremko wa Mstari
- Mteremko wa mstari ni\(m=\frac{\text{rise}}{\text{run}}\). Kuongezeka kwa hatua mabadiliko ya wima na kukimbia hatua za mabadiliko ya usawa.
- Slope-Intercept Fomu ya Equation ya Line
- Aina ya mteremka-intercept ya equation ya mstari na mteremko\(m\) na\(y\) -intercept,/((0, b)\) ni,\(y=mx+b\).
- Suluhisho la Ukosefu wa Linear
- Jozi kuamuru\((x,y)\) ni suluhisho la usawa linear kukosekana kwa usawa ni kweli wakati sisi badala ya maadili ya\(x\) na\(y\).
- Mstari wa wima
- Mstari wa wima ni grafu ya equation ya fomu\(x=a\). Mstari unapita kupitia\(x\) -axis saa\((a,0)\).
- X -kukatiza
- Hatua\((a,0)\) ambapo mstari unavuka\(x\) -axis;\(x\) -intercept hutokea wakati\(y\) ni sifuri.
- X -kuratibu
- Nambari ya kwanza katika jozi iliyoamriwa\((x,y)\).
- Y -kuratibu
- Nambari ya pili katika jozi iliyoamriwa\((x,y)\).
- Y -kukatiza
- Hatua\((0,b)\) ambapo mstari unavuka\(y\) -axis;\(y\) -intercept hutokea wakati\(x\) ni sifuri.