Straight Lines
Gbogbo ọrọ náà
Straight lines are the simplest curves in coordinate geometry, yet they carry an enormous amount of information. A single equation can describe every point on a line, predict where two lines cross, and reveal whether lines run parallel or meet at right angles. Mastering these ideas gives you a toolkit that appears in almost every other topic on the 4PM1 paper.
In this topic you will calculate gradients, write equations in several standard forms, and apply the conditions for parallel and perpendicular lines. Every technique translates directly into exam marks, so the worked examples follow the exact method that examiners reward.
Ebumnobi
- Calculate the gradient of a straight line joining two points
- Know and use the forms y = mx + c and y - y1 = m(x - x1) for the equation of a straight line
- Interpret ax + by = c as a straight line
- Determine the condition for two lines to be parallel or perpendicular
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E seela isiokwu a ka ị hụ otu echiche si ejikọta.
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Akwụkwọ Ọmụmụ
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Nnyocha Ọmụmụ
Ekele diri gi maka imecha ihe karịrị na Straight Lines. Ugbu a na ị na-enyochakwa isi echiche na echiche ndị dị mkpa, ọ bụ oge iji nwalee ihe ị ma. Ngwa a na-enye ụdị ajụjụ ọmụmụ dị iche iche emebere iji kwado nghọta gị wee nyere gị aka ịmata otú ị ghọtara ihe ndị a kụziri.
Ị ga-ahụ ngwakọta nke ụdị ajụjụ dị iche iche, gụnyere ajụjụ chọrọ ịhọrọ otu n’ime ọtụtụ azịza, ajụjụ chọrọ mkpirisi azịza, na ajụjụ ede ede. A na-arụpụta ajụjụ ọ bụla nke ọma iji nwalee akụkụ dị iche iche nke ihe ọmụma gị na nkà nke ịtụgharị uche.
Jiri akụkụ a nke nyocha ka ohere iji kụziere ihe ị matara banyere isiokwu ahụ ma chọpụta ebe ọ bụla ị nwere ike ịchọ ọmụmụ ihe ọzọ. Ekwela ka nsogbu ọ bụla ị na-eche ihu mee ka ị daa mba; kama, lee ha anya dị ka ohere maka ịzụlite onwe gị na imeziwanye.
- What is the gradient of the line joining (2, 3) and (6, 11)? A) 1/2 B) 2 C) 4 D) 8 Answer: B
- Which of the following lines is parallel to y = 5x - 3? A) y = -5x + 1 B) y = 5x + 7 C) y = x/5 + 2 D) y = -x/5 + 4 Answer: B
- Two perpendicular lines have gradients m1 and m2. Which equation must hold? A) m1 + m2 = 0 B) m1 = m2 C) m1 x m2 = -1 D) m1 x m2 = 1 Answer: C
- The line 4x + 2y = 10 has gradient: A) 4 B) 2 C) -2 D) -4 Answer: C
- A line passes through (0, 7) with gradient -3. What is its equation? A) y = -3x + 7 B) y = 3x + 7 C) y = -3x - 7 D) y = 7x - 3 Answer: A
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Akụkụ akwụkwọ
Linear Functions
Represent a linear function.
"College Algebra: Linear Functions" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/college-algebra/pages/4-1-linear-functions. Access for free at https://openstax.org/books/college-algebra/pages/1-introduction
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Meecha Ajụjụ Ule Ọmarịcha
Ị chọrọ ime ajụjụ ule ọmarịcha gbasara Straight Lines? Budata ngwa Green Bridge CBT iji nweta ajụjụ ule ọmarịcha na nyocha zuru ezu gbasara isiokwu a.
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