A line MN has a gradient of −2 and a y-intercept of −1. a) Write the equation of the line in the form y=mx+c…

Question

A line MN has a gradient of −2 and a y-intercept of −1. a) Write the equation of the line in the form y=mx+c. b) Generate a table of values using at least three points. c) Plot the values generated to draw the line.

ScanSolve AI Tutor · Accepted Answer

Huu hapa ni utatuzi wa swali lako: a) Andika mlinganyo wa mstari katika mfumo wa y = mx + c. Step 1: Tambua gradient na y-intercept. Kutoka kwa swali, tunapewa gradient (m) ni −2 na y-intercept (c) ni −1. Step 2: Badilisha maadili haya kwenye fomula ya mlinganyo wa mstari. Fomula ya mlinganyo wa mstari ni y = mx + c. y = (−2)x + (−1); y = −2x − 1; Mlinganyo wa mstari ni y = −2x − 1. b) Tengeneza jedwali la maadili ukitumia angalau pointi tatu. Step 1: Chagua maadili matatu ya x. Tutatumia maadili ya x = −1, 0, 1 kama ilivyo kwenye kazi yako. Step 2: Tumia mlinganyo y = −2x − 1 kupata maadili yanayolingana ya y. Kwa x = −1: y = −2(−1) − 1 = 2 − 1 = 1; Kwa x = 0: y = −2(0) − 1 = 0 − 1 = −1; Kwa x = 1: y = −2(1) − 1 = −2 − 1 = −3 Jedwali la maadili ni: |c|c|c|c| x & −1 & 0 & 1 y & 1 & −1 & −3 c) Chora maadili yaliyotengenezwa ili kuchora mstari. Step 1: Chora pointi kwenye grafu. Tumia jedwali la maadili kutoka sehemu (b) kuchora pointi zifuatazo kwenye grafu: Pointi ya kwanza: (−1, 1) Pointi ya pili: (0, −1) Pointi ya tatu: (1, −3) Step 2: Unganisha pointi kwa kutumia mstari ulionyooka. Baada ya kuchora pointi zote tatu, chora mstari ulionyooka unaopita kwenye pointi hizo. Mstari huu unawakilisha mlinganyo y = −2x − 1. Mchoro wako unaonyesha pointi zimechorwa kwa usahihi. Hatua inayofuata ni kuunganisha pointi hizo kwa mstari ulionyooka.

A line MN has a gradient of -2 and a y-intercept of -1. a) Write the equation of the line in the form y=mx+c. b) Generate a table of values using at least three points. c) Plot the values generated to draw the line.

Answer

Step-by-step solution

Part a· 2 steps

Tambua gradient na y-intercept.

Badilisha maadili haya kwenye fomula ya mlinganyo wa mstari.

Part b· 2 steps

Chagua maadili matatu ya $x$ .

Tumia mlinganyo $y = -2x - 1$ kupata maadili yanayolingana ya $y$ .

Part c· 2 steps

Chora pointi kwenye grafu.

Unganisha pointi kwa kutumia mstari ulionyooka.

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