Draw a Cartesian plane and label it from −10 to +10 on x-axis and −8 to +16 on y-axis.

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1. Chora ndege ya Cartesian na uweke lebo: Ili kuchora ndege ya Cartesian, chora mistari miwili inayopishana (x-axis na y-axis). Kwenye x-axis, weka lebo kutoka −10 hadi +10. Kwenye y-axis, weka lebo kutoka −8 hadi +16. Hakikisha umeweka alama za vitengo sawa kwenye kila mhimili. 2. Soma na uandike kuratibu za pointi P, Q, R, S, T na U: Kutoka kwenye ndege ya Cartesian uliyopewa, kuratibu za pointi ni: P: (−6, −3) Q: (−2, 7) R: (0, −5) S: (1, −2) T: (4, 3) U: (8, 0) 3. Tafuta na uweke pointi zifuatazo kwenye ndege ya Cartesian: Hizi ni kuratibu za pointi unazopaswa kuziweka kwenye ndege ya Cartesian: (i) A(0, −3) (ii) B(4, 6) (iii) C(−3, 2) (iv) D(−6, −3) (v) E(5, −4) (vi) F(−2, 10) (vii) G(1, 0) (viii) H(0, +5) 4. Unda jedwali la thamani kwa kila mlinganyo wa mstari uliotolewa: a) y − 2x + 4 = 0 Kwanza, tengeneza y iwe mada ya fomula: y = 2x − 4 Chagua thamani za x na uhesabu y: x — y = 2x − 4-2 — 2(−2) − 4 = −4 − 4 = −8; −1 — 2(−1) − 4 = −2 − 4 = −6; 0 — 2(0) − 4 = 0 − 4 = −4; 1 — 2(1) − 4 = 2 − 4 = −2; 2 — 2(2) − 4 = 4 − 4 = 0 Jedwali la thamani: x — −2 — −1 — 0 — 1 — 2y — −8 — −6 — −4 — −2 — 0 b) y + x = 3 Kwanza, tengeneza y iwe mada ya fomula: y = −x + 3 Chagua thamani za x na uhesabu y: x — y = −x + 3-2 — −(−2) + 3 = 2 + 3 = 5; −1 — −(−1) + 3 = 1 + 3 = 4; 0 — −(0) + 3 = 0 + 3 = 3; 1 — −(1) + 3 = −1 + 3 = 2; 2 — −(2) + 3 = −2 + 3 = 1 Jedwali la thamani: x — −2 — −1 — 0 — 1 — 2y — 5 — 4 — 3 — 2 — 1 5. Jaza jedwali kwa kutumia mlinganyo y = 1/2x − 4 na uamue kipimo kinachofaa: Step 1: Jaza jedwali. Tumia mlinganyo y = 1/2x − 4 kwa kila thamani ya x: Kwa x = 10: y = 1/2(10) − 4 = 5 − 4 = 1; Kwa x = 20: y = 1/2(20) − 4 = 10 − 4 = 6; Kwa x = 30: y = 1/2(30) − 4 = 15 − 4 = 11; Kwa x = 40: y = 1/2(40) − 4 = 20 − 4 = 16; Kwa x = 50: y = 1/2(50) − 4 = 25 − 4 = 21; Kwa x = 60: y = 1/2(60) − 4 = 30 − 4 = 26 Jedwali lililojazwa: x — 10 — 20 — 30 — 40 — 50 — 60y — 1 — 6 — 11 — 16 — 21 — 26 Step 2: Amua kipimo kinachofaa. Thamani za x zinaanzia 10 hadi 60, na thamani za y zinaanzia 1 hadi 26. Kwa x-axis: Kipimo kinachofaa kinaweza kuwa 1 kitengo = 10 vitengo. Kwa y-axis: Kipimo kinachofaa kinaweza kuwa 1 kitengo = 5 vitengo.

$x$	$y = 2x - 4$
-2	$2(-2) - 4 = -4 - 4 = -8$
-1	$2(-1) - 4 = -2 - 4 = -6$
0	$2(0) - 4 = 0 - 4 = -4$
1	$2(1) - 4 = 2 - 4 = -2$
2	$2(2) - 4 = 4 - 4 = 0$

$x$	$y = -x + 3$
-2	$-(-2) + 3 = 2 + 3 = 5$
-1	$-(-1) + 3 = 1 + 3 = 4$
0	$-(0) + 3 = 0 + 3 = 3$
1	$-(1) + 3 = -1 + 3 = 2$
2	$-(2) + 3 = -2 + 3 = 1$

Draw a Cartesian plane and label it from -10 to +10 on x-axis and -8 to +16 on y-axis.

Answer

Step-by-step solution

Part i

Part ii

Part iii

Part iv

Part v

Part vi

Part vii

Part viii

Part a

Part b· 2 steps
$\mathbf{1 \text{ kitengo} = 10 \text{ vitengo}}$

Jaza jedwali.

Amua kipimo kinachofaa.

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