4.6E: Mazoezi

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Mazoezi hufanya kamili

Kupata Equation ya Line Kutokana na mteremko na$y$ - Intercept

Katika mazoezi yafuatayo, pata usawa wa mstari na mteremko uliopewa na$y$ -intercept. Andika equation katika mteremka-intercept fomu.

Zoezi$\PageIndex{1}$

mteremko$3$ na$y$ -kukatiza$(0,5)$

Zoezi$\PageIndex{2}$

mteremko$4$ na$y$ -kukatiza$(0,1)$

Jibu: $y=4x+1$

Zoezi$\PageIndex{3}$

mteremko$6$ na$y$ -kukatiza$(0,−4)$

Zoezi$\PageIndex{4}$

mteremko$8$ na$y$ -kukatiza$(0,−6)$

Jibu: $y=8x−6$

Zoezi$\PageIndex{5}$

mteremko$−1$ na$y$ -kukatiza$(0,3)$

Zoezi$\PageIndex{6}$

mteremko$−1$ na$y$ -kukatiza$(0,7)$

Jibu: $y=−x+7$

Zoezi$\PageIndex{7}$

mteremko$−2$ na$y$ -kukatiza$(0,−3)$

Zoezi$\PageIndex{8}$

mteremko$−3$ na$y$ -kukatiza$(0,−1)$

Jibu: $y=−3x−1$

Zoezi$\PageIndex{9}$

mteremko$\frac{3}{5}$ na$y$ -kukatiza$(0,-1)$

Zoezi$\PageIndex{10}$

mteremko$\frac{1}{5}$ na$y$ -kukatiza$(0,-5)$

Jibu: $y=\frac{1}{5} x-5$

Zoezi$\PageIndex{11}$

mteremko$-\frac{3}{4}$ na$y$ -kukatiza$(0,-2)$

Zoezi$\PageIndex{12}$

mteremko$-\frac{2}{3}$ na$y$ -kukatiza$(0,-3)$

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

Zoezi$\PageIndex{13}$

mteremko$0$ na$y$ -kukatiza$(0,-1)$

Zoezi$\PageIndex{14}$

mteremko$0$ na$y$ -kukatiza$(0,2)$

Jibu: $y=2$

Zoezi$\PageIndex{15}$

mteremko$-3$ na$y$ -kukatiza$(0,0)$

Zoezi$\PageIndex{16}$

mteremko$-4$ na$y$ -kukatiza$(0,0)$

Jibu: $y=−4x$

Katika mazoezi yafuatayo, pata usawa wa mstari ulioonyeshwa kwenye kila grafu. Andika equation katika mteremka-intercept fomu.

Zoezi$\PageIndex{17}$

$Grafu inaonyesha ndege ya kuratibu x y. Ya x na y-axes kila kukimbia kutoka hasi 9 hadi 9. Hatua (1, hasi 2) imepangwa. Mstari unachukua mhimili wa y saa (0, hasi 5), hupita kupitia hatua (1, hasi 2), na huchukua x-axis saa (theluthi 5, 0).$

Zoezi$\PageIndex{18}$

$Grafu inaonyesha ndege ya kuratibu x y. Ya x na y-axes kila kukimbia kutoka hasi 9 hadi 9. Hatua (2, 0) imepangwa. Mstari unachukua mhimili wa y saa (0, 4) na huchukua x-axis saa (2, 0).$

Jibu: $y=−2x+4$

Zoezi$\PageIndex{19}$

$Grafu inaonyesha ndege ya kuratibu x y. Ya x na y-axes kila kukimbia kutoka hasi 9 hadi 9. Hatua (6, 0) imepangwa. Mstari unachukua mhimili wa y saa (0, hasi 3) na huchukua x-axis saa (6, 0).$

Zoezi$\PageIndex{20}$

$Grafu inaonyesha ndege ya kuratibu x y. Ya x na y-axes kila kukimbia kutoka hasi 9 hadi 9. Hatua (4, 5) imepangwa. Mstari unachukua x-axis katika (hasi 8 theluthi, 0), inakataza y mhimili katika (0, 2), na hupita kupitia hatua (4, 5).$

Jibu: $y=\frac{3}{4} x+2$

Zoezi$\PageIndex{21}$

$Grafu inaonyesha ndege ya kuratibu x y. Ya x na y-axes kila kukimbia kutoka hasi 9 hadi 9. Hatua (3, hasi 1) imepangwa. Mstari unachukua mhimili wa y saa (0, 2), huchukua x-axis saa (9 nne, 0), na hupita kupitia hatua (3, hasi 1).$

Zoezi$\PageIndex{22}$

$Grafu inaonyesha ndege ya kuratibu x y. Ya x na y-axes kila kukimbia kutoka hasi 9 hadi 9. Hatua (2, hasi 4) imepangwa. Mstari unachukua x-axis katika (hasi 2 theluthi, 0), inakataza y mhimili saa (0, hasi 1), na hupita kupitia hatua (2, hasi 4).$

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

Zoezi$\PageIndex{23}$

$Grafu inaonyesha ndege ya kuratibu x y. Ya x na y-axes kila kukimbia kutoka hasi 9 hadi 9. Hatua (2, hasi 2) imepangwa. Mstari unaoendana na mhimili wa x huchukua mhimili wa y saa (0, hasi 2) na hupita kupitia hatua (2, hasi 2).$

Zoezi$\PageIndex{24}$

$Grafu inaonyesha ndege ya kuratibu x y. Ya x na y-axes kila kukimbia kutoka hasi 9 hadi 9. Hatua (hasi 3, 6) imepangwa. Mstari unaoendana na mhimili wa x hupita kupitia (hasi 3, 6) na huchukua mhimili wa y saa (0, 6).$

Jibu: $y=6$

Kupata Equation ya Line Kutokana na mteremko na Point

Katika mazoezi yafuatayo, pata usawa wa mstari na mteremko uliopewa na una uhakika uliopewa. Andika equation katika mteremka-intercept fomu.

Zoezi$\PageIndex{25}$

$m=\frac{5}{8},$elekeza$(8,3)$

Zoezi$\PageIndex{26}$

$m=\frac{3}{8},$elekeza$(8,2)$

Jibu: $y=\frac{3}{8} x-1$

Zoezi$\PageIndex{27}$

$m=\frac{1}{6},$elekeza$(6,1)$

Zoezi$\PageIndex{28}$

$m=\frac{5}{6},$elekeza$(6,7)$

Jibu: $y=\frac{5}{6} x+2$

Zoezi$\PageIndex{29}$

$m=-\frac{3}{4},$elekeza$(8,-5)$

Zoezi$\PageIndex{30}$

$m=-\frac{3}{5},$elekeza$(10,-5)$

Jibu: $y=-\frac{3}{5} x+1$

Zoezi$\PageIndex{31}$

$m=-\frac{1}{4},$elekeza$(-12,-6)$

Zoezi$\PageIndex{32}$

$m=-\frac{1}{3},$elekeza$(-9,-8)$

Jibu: $y=-\frac{1}{3} x-11$

Zoezi$\PageIndex{33}$

Mstari wa usawa ulio na$(−2,5)$

Zoezi$\PageIndex{34}$

Mstari wa usawa ulio na$(−1,4)$

Jibu: $y=4$

Zoezi$\PageIndex{35}$

Mstari wa usawa ulio na$(−2,−3)$

Zoezi$\PageIndex{36}$

Mstari wa usawa ulio na$(−1,−7)$

Jibu: $y=−7$

Zoezi$\PageIndex{37}$

$m=-\frac{3}{2},$elekeza$(-4,-3)$

Zoezi$\PageIndex{38}$

$m=-\frac{5}{2},$elekeza$(-8,-2)$

Jibu: $y=-\frac{5}{2} x-22$

Zoezi$\PageIndex{39}$

$m=-7,$elekeza$(-1,-3)$

Zoezi$\PageIndex{40}$

$m=-4,$elekeza$(-2,-3)$

Jibu: $y=-4 x-11$

Zoezi$\PageIndex{41}$

Mstari wa usawa ulio na$(2,-3)$

Zoezi$\PageIndex{42}$

Mstari wa usawa ulio na$(4,-8)$

Jibu: $y=−8$

Kupata Equation ya Line Kutokana Pointi mbili

Katika mazoezi yafuatayo, pata usawa wa mstari ulio na pointi zilizopewa. Andika equation katika mteremka-intercept fomu.

Zoezi$\PageIndex{43}$

$(2,6)$na$(5,3)$

Zoezi$\PageIndex{44}$

$(3,1)$na$(2,5)$

Jibu: $y=−4x+13$

Zoezi$\PageIndex{45}$

$(4,3)$na$(8,1)$

Zoezi$\PageIndex{46}$

$(2,7)$na$(3,8)$

Jibu: $y=x+5$

Zoezi$\PageIndex{47}$

$(−3,−4)$na$(5−2)$

Zoezi$\PageIndex{48}$

$(−5,−3)$na$(4,−6)$

Jibu: $y=-\frac{1}{3} x-\frac{14}{3}$

Zoezi$\PageIndex{49}$

$(−1,3)$na$(−6,−7)$

Zoezi$\PageIndex{50}$

$(−2,8)$na$(−4,−6)$

Jibu: $y=7x+22$

Zoezi$\PageIndex{51}$

$(6,−4)$na$(−2,5)$

Zoezi$\PageIndex{52}$

$(3,−2)$na$(−4,4)$

Jibu: $y=-\frac{6}{7} x+\frac{4}{7}$

Zoezi$\PageIndex{53}$

$(0,4)$na$(2,−3)$

Zoezi$\PageIndex{54}$

$(0,−2)$na$(−5,−3)$

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

Zoezi$\PageIndex{55}$

$(7,2)$na$(7,−2)$

Zoezi$\PageIndex{56}$

$(4,2)$na$(4,−3)$

Jibu: $x=4$

Zoezi$\PageIndex{57}$

$(−7,−1)$na$(−7,−4)$

Zoezi$\PageIndex{58}$

$(−2,1)$na$(−2,−4)$

Jibu: $x=−2$

Zoezi$\PageIndex{59}$

$(6,1)$na$(0,1)$

Zoezi$\PageIndex{60}$

$(6,2)$na$(−3,2)$

Jibu: $y=2$

Zoezi$\PageIndex{61}$

$(3,−4)$na$(5,−4)$

Zoezi$\PageIndex{62}$

$(−6,−3)$na$(−1,−3)$

Jibu: $y=−3$

Zoezi$\PageIndex{63}$

$(4,3)$na$(8,0)$

Zoezi$\PageIndex{64}$

$(0,0)$na$(1,4)$

Jibu: $y=4x$

Zoezi$\PageIndex{65}$

$(−2,−3)$na$(−5,−6)$

Zoezi$\PageIndex{66}$

$(−3,0)$na$(−7,−2)$

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

Zoezi$\PageIndex{67}$

$(8,−1)$na$(8,−5)$

Zoezi$\PageIndex{68}$

$(3,5)$na$(−7,5)$

Jibu: $y=5$

Pata Equation ya Mstari Sambamba na Line Iliyopewa

Katika mazoezi yafuatayo, pata usawa wa mstari unaofanana na mstari uliopewa na una uhakika uliopewa. Andika equation katika mteremka-intercept fomu.

Zoezi$\PageIndex{69}$

$y=4 x+2,$uhakika wa mstari$(1,2)$

Zoezi$\PageIndex{70}$

$y=3 x+4,$uhakika wa mstari$(2,5)$

Jibu: $y=3 x-1$

Zoezi$\PageIndex{71}$

$y=-2 x-3,$uhakika wa mstari$(-1,3)$

Zoezi$\PageIndex{72}$

$y=-3x-1,$uhakika wa mstari$(2,-3)$

Jibu: $y=−3x+3$

Zoezi$\PageIndex{73}$

$3 x-y=4,$uhakika wa mstari$(3,1)$

Zoezi$\PageIndex{74}$

$2 x-y=6,$uhakika wa mstari$(3,0)$

Jibu: $y=2x−6$

Zoezi$\PageIndex{75}$

$4 x+3 y=6,$uhakika wa mstari$(0,-3)$

Zoezi$\PageIndex{76}$

$2x+3y=6,$uhakika wa mstari$(0,5)$

Jibu: $y=-\frac{2}{3} x+5$

Zoezi$\PageIndex{77}$

$x=-3,$uhakika wa mstari$(-2,-1)$

Zoezi$\PageIndex{78}$

$x=-4,$uhakika wa mstari$(-3,-5)$

Jibu: $x=−3$

Zoezi$\PageIndex{79}$

$x-2=0,$uhakika wa mstari$(1,-2)$

Zoezi$\PageIndex{80}$

$x-6=0,$uhakika wa mstari$(4,-3)$

Jibu: $x=4$

Zoezi$\PageIndex{81}$

$y=5,$uhakika wa mstari$(2,-2)$

Zoezi$\PageIndex{82}$

$y=1,$uhakika wa mstari$(3,-4)$

Jibu: $y=−4$

Zoezi$\PageIndex{83}$

$y+2=0,$uhakika wa mstari$(3,-3)$

Zoezi$\PageIndex{84}$

$y+7=0,$uhakika wa mstari$(1,-1)$

Jibu: $y=−1$

Kupata Equation ya Line Perpendicular kwa Line Kutokana

Katika mazoezi yafuatayo, pata equation ya mstari perpendicular kwa mstari uliopewa na ina uhakika fulani. Andika equation katika mteremka-intercept fomu.

Zoezi$\PageIndex{85}$

$y=-2 x+3,$uhakika wa mstari$(2,2)$

Zoezi$\PageIndex{86}$

$y=-x+5,$uhakika wa mstari$(3,3)$

Jibu: $y=x$

Zoezi$\PageIndex{87}$

$y=\frac{3}{4} x-2,$uhakika wa mstari$(-3,4)$

Zoezi$\PageIndex{88}$

$y=\frac{2}{3} x-4,$uhakika wa mstari$(2,-4)$

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

Zoezi$\PageIndex{89}$

$2 x-3 y=8,$uhakika wa mstari$(4,-1)$

Zoezi$\PageIndex{90}$

$4 x-3 y=5,$uhakika wa mstari$(-3,2)$

Jibu: $y=-\frac{3}{4} x-\frac{1}{4}$

Zoezi$\PageIndex{91}$

$2 x+5 y=6,$uhakika wa mstari$(0,0)$

Zoezi$\PageIndex{92}$

$4 x+5 y=-3,$uhakika wa mstari$(0,0)$

Jibu: $y=\frac{5}{4} x$

Zoezi$\PageIndex{93}$

$y-3=0,$uhakika wa mstari$(-2,-4)$

Zoezi$\PageIndex{94}$

$y-6=0,$uhakika wa mstari$(-5,-3)$

Jibu: $x=-5$

Zoezi$\PageIndex{95}$

mstari$y$ -axis, uhakika$(3,4)$

Zoezi$\PageIndex{96}$

mstari$y$ -axis, uhakika$(2,1)$

Jibu: $y=1$

Mazoezi ya mchanganyiko

Katika mazoezi yafuatayo, pata usawa wa kila mstari. Andika equation katika mteremka-intercept fomu.

Zoezi$\PageIndex{97}$

Ina pointi$(4,3)$ na$(8,1)$

Zoezi$\PageIndex{98}$

Ina pointi$(2,7)$ na$(3,8)$

Jibu: $y=x+5$

Zoezi$\PageIndex{99}$

$m=\frac{1}{6},$iliyo na uhakika$(6,1)$

Zoezi$\PageIndex{100}$

$m=\frac{5}{6},$iliyo na uhakika$(6,7)$

Jibu: $y=\frac{5}{6} x+2$

Zoezi$\PageIndex{101}$

Sambamba na mstari$4 x+3 y=6,$ ulio na uhakika$(0,-3)$

Zoezi$\PageIndex{102}$

Sambamba na mstari$2 x+3 y=6,$ ulio na uhakika$(0,5)$

Jibu: $y=-\frac{2}{3} x+5$

Zoezi$\PageIndex{103}$

$m=-\frac{3}{4},$iliyo na uhakika$(8,-5)$

Zoezi$\PageIndex{104}$

$m=-\frac{3}{5},$iliyo na uhakika$(10,-5)$

Jibu: $y=-\frac{3}{5} x+1$

Zoezi$\PageIndex{105}$

Perpendicular kwa$y-1=0,$ uhakika line$(-2,6)$

Zoezi$\PageIndex{106}$

Perpendicular kwa mstari y-axis, uhakika$(-6,2)$

Jibu: $y=2$

Zoezi$\PageIndex{107}$

Ina pointi$(4,3)$ na$(8,1)$

Zoezi$\PageIndex{108}$

Ina pointi$(-2,0)$ na$(-3,-2)$

Jibu: $y=x+2$

Zoezi$\PageIndex{109}$

Sambamba na mstari$x=-3,$ ulio na uhakika$(-2,-1)$

Zoezi$\PageIndex{110}$

Sambamba na mstari$x=-4,$ ulio na uhakika$(-3,-5)$

Jibu: $x=-3$

Zoezi$\PageIndex{111}$

Ina pointi$(-3,-4)$ na$(2,-5)$

Zoezi$\PageIndex{112}$

Ina pointi$(-5,-3)$ na$(4,-6)$

Jibu: $y=-\frac{1}{3} x-\frac{14}{3}$

Zoezi$\PageIndex{113}$

Perpendicular kwa line$x-2 y=5,$ zenye uhakika$(-2,2)$

Zoezi$\PageIndex{114}$

Perpendicular kwa line$4 x+3 y=1,$ zenye uhakika$(0,0)$

Jibu: $y=\frac{3}{4} x$

kila siku Math

Zoezi$\PageIndex{115}$

Cholesterol. umri,$x,$ na LDL cholesterol ngazi,$y,$ ya watu wawili ni kutolewa$(18,68)$ na pointi na$(27,122) .$ Kupata equation linear kwamba mifano ya uhusiano kati ya umri na LDL cholesterol ngazi.

Zoezi$\PageIndex{116}$

Matumizi ya mafuta. mji mpg,$x$, na barabara kuu mpg,$y,$ ya magari mawili hutolewa$(29,40)$ na pointi na$(19,28) .$ Kupata
equation linear kwamba mifano ya uhusiano kati ya mji mpg na barabara mbunge.

Jibu: $y=1.2 x+5.2$

Mazoezi ya kuandika

Zoezi$\PageIndex{117}$

Kwa nini mistari yote ya usawa inafanana?

Zoezi$\PageIndex{118}$

Eleza kwa maneno yako mwenyewe kwa nini mteremko wa mistari miwili ya perpendicular lazima iwe na ishara tofauti.

Jibu: Majibu yatatofautiana.

Self Check

Baada ya kukamilisha mazoezi, tumia orodha hii ili kutathmini ujuzi wako wa malengo ya sehemu hii.

$Hii ni meza ambayo ina safu sita na nguzo nne. Katika mstari wa kwanza, ambayo ni mstari wa kichwa, seli zinasoma kutoka kushoto kwenda kulia: “Ninaweza...,” “kwa ujasiri,” “kwa msaada fulani,” na “Hakuna-siipati!” Safu ya kwanza chini ya “naweza...” inasoma “tafuta equation ya mstari uliotolewa mteremko na y-intercept,”, “tafuta equation ya mstari uliotolewa mteremko na hatua,” “pata equation ya mstari uliopewa pointi mbili,” “pata equation ya mstari sambamba na mstari uliopewa,” na “pata equation ya mstari perpendicular kwa mstari fulani.” Wengine wa seli ni tupu.$

b Kwa kiwango cha 1-10, ungewezaje kupima ujuzi wako wa sehemu hii kwa kuzingatia majibu yako kwenye orodha? Unawezaje kuboresha hii?

Mazoezi hufanya kamili

Zoezi\(\PageIndex{1}\)

Zoezi\(\PageIndex{2}\)

Zoezi\(\PageIndex{3}\)

Zoezi\(\PageIndex{4}\)

Zoezi\(\PageIndex{5}\)

Zoezi\(\PageIndex{6}\)

Zoezi\(\PageIndex{7}\)

Zoezi\(\PageIndex{8}\)

Zoezi\(\PageIndex{9}\)

Zoezi\(\PageIndex{10}\)

Zoezi\(\PageIndex{11}\)

Zoezi\(\PageIndex{12}\)

Zoezi\(\PageIndex{13}\)

Zoezi\(\PageIndex{14}\)

Zoezi\(\PageIndex{15}\)

Zoezi\(\PageIndex{16}\)

Zoezi\(\PageIndex{17}\)

Zoezi\(\PageIndex{18}\)

Zoezi\(\PageIndex{19}\)

Zoezi\(\PageIndex{20}\)

Zoezi\(\PageIndex{21}\)

Zoezi\(\PageIndex{22}\)

Zoezi\(\PageIndex{23}\)

Zoezi\(\PageIndex{24}\)

Zoezi\(\PageIndex{25}\)

Zoezi\(\PageIndex{26}\)

Zoezi\(\PageIndex{27}\)

Zoezi\(\PageIndex{28}\)

Zoezi\(\PageIndex{29}\)

Zoezi\(\PageIndex{30}\)

Zoezi\(\PageIndex{31}\)

Zoezi\(\PageIndex{32}\)

Zoezi\(\PageIndex{33}\)

Zoezi\(\PageIndex{34}\)

Zoezi\(\PageIndex{35}\)

Zoezi\(\PageIndex{36}\)

Zoezi\(\PageIndex{37}\)

Zoezi\(\PageIndex{38}\)

Zoezi\(\PageIndex{39}\)

Zoezi\(\PageIndex{40}\)

Zoezi\(\PageIndex{41}\)

Zoezi\(\PageIndex{42}\)

Zoezi\(\PageIndex{43}\)

Zoezi\(\PageIndex{44}\)

Zoezi\(\PageIndex{45}\)

Zoezi\(\PageIndex{46}\)

Zoezi\(\PageIndex{47}\)

Zoezi\(\PageIndex{48}\)

Zoezi\(\PageIndex{49}\)

Zoezi\(\PageIndex{50}\)

Zoezi\(\PageIndex{51}\)

Zoezi\(\PageIndex{52}\)

Zoezi\(\PageIndex{53}\)

Zoezi\(\PageIndex{54}\)

Zoezi\(\PageIndex{55}\)

Zoezi\(\PageIndex{56}\)

Zoezi\(\PageIndex{57}\)

Zoezi\(\PageIndex{58}\)

Zoezi\(\PageIndex{59}\)

Zoezi\(\PageIndex{60}\)

Zoezi\(\PageIndex{61}\)

Zoezi\(\PageIndex{62}\)

Zoezi\(\PageIndex{63}\)

Zoezi\(\PageIndex{64}\)

Zoezi\(\PageIndex{65}\)

Zoezi\(\PageIndex{66}\)

Zoezi\(\PageIndex{67}\)

Zoezi\(\PageIndex{68}\)

Zoezi\(\PageIndex{69}\)

Zoezi\(\PageIndex{70}\)

Zoezi\(\PageIndex{71}\)

Zoezi\(\PageIndex{72}\)

Zoezi\(\PageIndex{73}\)

Zoezi\(\PageIndex{74}\)

Zoezi\(\PageIndex{75}\)

Zoezi\(\PageIndex{76}\)

Zoezi\(\PageIndex{77}\)

Zoezi\(\PageIndex{78}\)

Zoezi\(\PageIndex{79}\)