Xác định a, b để đồ thị hàm số y = ax + b đi qua hai điểm hay viết phương trình hàm số bậc nhât đi qua hai điểm (viết phương trình đường thẳng đi qua hai điểm) là dạng bài tập các em hay gặp ở nội dung toán lớp 9.
Vậy cách xác định a, b để đồ thị hàm số y = ax + b đi qua hai điểm như thế nào? cách viết phương trình đường thẳng đi qua hai điểm ra sao? chúng ta cùng tìm hiểu qua bài viết dưới đây.
° Xác định a, b để đồ thị hàm số đi qua 2 điểm (viết phương trình đường thẳng đi qua 2 điểm cho trước).
– Cho tọa độ 2 điểm A, B trong hệ Oxy. Hãy xác định hệ số a, b để đồ thị hàm số bậc nhất đi qua 2 điểm (hay viết phương trình đường thẳng đi qua 2 điểm A, B) ta thực hiện các bước sau:
– Bước 1: Gọi tổng quát đường thẳng có dạng y = ax + b (a khác 0)
– Bước 2: Với từng điểm cho trước thì thay trực tiếp vào phương trình đường thẳng. Khi đó, ta được 2 phương trình bậc nhất.
– Bước 3: Giải hệ phương trình tìm a và b
– Bước 4: Viết phương trình đồ thị hàm số (viết phương trình đường thẳng)
° Ví dụ minh họa cách xác định a, b để đồ thị hàm số đi qua 2 điểm (viết phương trình đường thẳng đi qua 2 điểm cho trước).
* Ví dụ 1: Xác định a và b để đồ thị hàm số y = ax + b đi qua hai điểm A(2; -2) và B(-1; 3).
* Lời giải:
– Đồ thị hàm số y = ax + b đi qua A(2; -2) nên ta có: 2.a + b = -2 (1)
– Đồ thị hàm số y = ax + b đi qua B(-1; 3) nên ta có: (-1).a + b = 3 (2)
Từ (1) và (2) ta có hệ phương trình:
Vậy đồ thị hàm số có dạng: 
* Ví dụ 2: Xác định a và b để đồ thị hàm số bậc nhất y = ax + b đi qua hai điểm A(1; 3) và B(-1; -1)
* Lời giải:
– Đồ thị hàm số y = ax + b đi qua A(1; 3) nên ta có: 1.a + b = 3 (1)
– Đồ thị hàm số y = ax + b đi qua B(-1; -1) nên ta có: (-1).a + b = -1 (2)
Từ (1) và (2) ta có hệ phương trình:
Vậy đồ thị hàm số có dạng: y = 2x + 1.
* Ví dụ 3: Xác định hàm số bậc nhất biết đồ thị là đường thẳng đi qua 2 điểm A(1; 2) và B(-2; 3).
* Lời giải:
– Đồ thị hàm số (phương trình đường thẳng dạng tổng quát) y = ax + b đi qua A(1; 2) nên ta có: 1.a + b = 2 (1)
– Đồ thị hàm số y = ax + b đi qua B(-2; 3) nên ta có: (-2).a + b = 3 (2)
Từ (1) và (2) ta có hệ phương trình:
Vậy đồ thị hàm số có dạng: 
Hy vọng với bài viết xác định a, b để đồ thị hàm số y = ax + b đi qua hai điểm hay viết phương trình hàm số bậc nhất đi qua hai điểm (viết phương trình đường thẳng đi qua hai điểm) ở nội dung toán lớp 9 trên của Trường TCSP Mẫu giáo – Nhà trẻ Hà Nội giúp các em giải các bài tập dạng này một cách dễ dàng. Mọi góp ý và thắc mắc các em hãy để lại nhận xét dưới bài viết để Hay Học Hỏi ghi nhận và hỗ trợ, chúc các em học tốt.
Bản quyền bài viết thuộc trường trung học phổ thông Sóc Trăng. Mọi hành vi sao chép đều là gian lận.
Nguồn chia sẻ: Trường THPT Thành Phố Sóc Trăng (thptsoctrang.edu.vn)
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