7.4: Ulinganisho wa mistari ya Wima na ya usawa

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Page ID: 164592

Victoria Dominguez, Cristian Martinez, and Sanaa Saykali
Citrus College via ASCCC Open Educational Resources Initiative

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Ufafanuzi: Line ya Wima

Ulinganisho wa mstari wa wima ni wa fomu$x = c$, wapi$c$ nambari yoyote halisi. Mstari wa wima daima utazunguka$x$ -axis kwa uhakika$(c, 0)$. Mteremko wa mstari wa wima haujafafanuliwa.

Mfano Template:index

Pata mteremko wa mstari$x = 4$ na graph mstari.

Suluhisho

$x = 4$ni grafu ya mstari wa wima kama inavyoonekana katika takwimu hapa chini.

$clipboard_e96383c84992a62541d09b7ee1e53697f.png$

Ili kupata mteremko wa mstari$x = 4$ chagua pointi mbili tofauti kwenye mstari. Hebu pointi ziwe$(4, −1)$ na$(4, 3)$. Kutumia mteremko wa fomu ya mstari,

$\begin{array} &&m = \dfrac{y_2 − y_1}{x_2 − x_1} &\text{The slope of a line formula} \\ &= \dfrac{3 − (−1)}{4 − 4} &\text{Substitute values} \\ &= \dfrac{4}{0} &\text{Simplify} \end{array}$

Sasa, ikiwa$4$ imegawanywa na$0$, hii ni sawa na kuuliza swali,” ni namba gani mara zero inatoa$4$?” jibu ni, hakuna idadi hiyo. Idara ya sifuri haijulikani, na mteremko wa mstari wa wima$x = 4$ haujafafanuliwa.

Ufafanuzi: Line ya usawa

Ulinganisho wa mstari usio na usawa ni wa fomu$y = k$, wapi$k$ nambari yoyote halisi. Mstari wa usawa utazunguka kila wakati$y$ -axis kwa uhakika$(0, k)$. Mteremko wa mstari usio na usawa ni Zero.

Mfano Template:index

Pata mteremko wa mstari unaopita kupitia pointi$(−3, −2)$ na$(4, −2)$. Panda pointi na grafu mstari unaopita kupitia kwao.

Suluhisho

Tumia mteremko wa fomu ya mstari. Hivyo,

$\begin{array} &&m = \dfrac{y_2 − y_1}{x_2 − x_1} &\text{The slope of a line formula} \\ &= \dfrac{(−2) − (−2)}{4 − (−3)} &\text{Substitute values} \\ &= \dfrac{0}{7} &\text{Simplify} \\ &= 0 &\text{\(0$imegawanywa na nambari yoyote isiyo ya zero ni sawa na sifuri}\ mwisho {array}\)

Kwa hiyo, mstari unaopita kupitia pointi mbili zilizopewa ni mstari wa usawa, na mteremko sawa na sifuri, kama inavyoonekana katika takwimu hapa chini.

$clipboard_e08cf4386944def611c6831ac921a6f6d.png$

Mfano Template:index

Graph mstari$y − 3 = 0$ na kupata mteremko wake.

Suluhisho

Mstari$y − 3 = 0$ unaweza kuandikwa kama$y = 3$ ($3$kuongeza pande zote mbili za equation). Mstari$y = 3$ ni mstari usio na usawa, kama inavyoonekana katika takwimu hapa chini.

$clipboard_ef5d1c3aa2712f38f53b81ce34e7a1ee0.png$

Sasa, ili kupata mteremko, chagua pointi mbili tofauti kwenye mstari$y = 3$. Fikiria pointi$(0, 3)$ na$(3, 3)$. Hivyo,

$\begin{array} &&m = \dfrac{y_2 − y_1}{x_2 − x_1} &\text{The slope of a line formula} \\ &= \dfrac{3-3}{3-0} &\text{Substitute values} \\ &= \dfrac{0}{2} &\text{Simplify} \\ &= 0 &\text{\(0$imegawanywa na nambari yoyote isiyo ya zero ni sawa na sifuri}\ mwisho {array}\)

Kwa hiyo, mteremko wa mstari uliopewa ni$m = 0.$

Zoezi Template:index

Pata mteremko wa kila mstari.

$x = −\dfrac{1}{2}$
$y − 1 = 0$
$x + 7 = 10$
$y + 2 = −9$
Pata mteremko wa mstari unaopita kupitia pointi$(−4, 1)$ na$(2, 1)$. Panda pointi na grafu mstari unaopita kupitia kwao.
Pata mteremko wa mstari unaopita kupitia pointi$(−3, 5)$ na$(−3, −7)$. Panda pointi na grafu mstari unaopita kupitia kwao.