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Giải bài 7.33 trang 33 sách bài tập toán 8 - Kết nối tri thức với cuộc sống

Tìm hàm số bậc nhất có đồ thị là đường thẳng đi qua điểm (1; 2) và có hệ số góc là \( - 3.\)

♊Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Khoa học tự nhiên
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Đề bài

Tìm hàm số bậc nhất có đồ thị là đường thẳng đi qua điểm (1; 2) và có hệ số góc là \( - 3.\)

Phương pháp giải - Xem chi tiết

ꦍ+ Sử dụng khái niệm hệ số góc của đường thẳng để viết hàm số bậc nhất: Ta gọi a là hệ số góc của đường thẳng \(y = ax + b\left( {a \ne 0} \right)\)

+ Thay tọa độ của điểm (1; 2) vào hàm số từ đó tìm được b.

Lời giải chi tiết

Giả sử hàm số bậc nhất có dạng \(y = ax + b\left( {a \ne 0} \right)\)Vì hàm số bậc nhất \(y = ax + b\left( {a \ne 0} \right)\) có đồ thị là đường thẳng có hệ số góc bằng \( - 3\) nên \(a =  - 3\) (thỏa mãn). Do đó, \(y =  - 3x + b\)Lại có, đồ thị hàm số \(y =  - 3x + b\) đi qua điểm (1; 2) nên ta có:\(2 =  - 3.1 + b\)\(b = 5\)Do đó, hàm số cần tìm là: \(y =  - 3x + 5\)

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