Straight Lines
Bayani Gaba-gaba
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.
Manufura
- 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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Takardar Darasi
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Nazarin Darasi
Barka da kammala darasi akan Straight Lines. Yanzu da kuka bincika mahimman raayoyi da raayoyi, lokaci yayi da zaku gwada ilimin ku. Wannan sashe yana ba da ayyuka iri-iri Tambayoyin da aka tsara don ƙarfafa fahimtar ku da kuma taimaka muku auna fahimtar ku game da kayan.
Za ka gamu da haɗe-haɗen nau'ikan tambayoyi, ciki har da tambayoyin zaɓi da yawa, tambayoyin gajeren amsa, da tambayoyin rubutu. Kowace tambaya an ƙirƙira ta da kyau don auna fannoni daban-daban na iliminka da ƙwarewar tunani mai zurfi.
Yi wannan ɓangaren na kimantawa a matsayin wata dama don ƙarfafa fahimtarka kan batun kuma don gano duk wani yanki da kake buƙatar ƙarin karatu. Kada ka yanke ƙauna da duk wani ƙalubale da ka fuskanta; maimakon haka, ka kallesu a matsayin damar haɓaka da ingantawa.
- 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
Yi aikin wadannan tambayoyi a cikin manhaja
Yi aikin wadannan tambayoyi a cikin manhaja
Littattafan da ake ba da shawarar karantawa
Ƙarin koyo daga tushe na buɗe
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Sashen littafi
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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