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Giải bài 7.34 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 với hệ số góc là 2 và cắt trục hoành tại điểm có hoành độ bằng \( - 3\)

🌄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 với hệ số góc là 2 và cắt trục hoành tại điểm có hoành độ bằng \( - 3\)

Phương pháp giải - Xem chi tiết

+ 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 \(y = ax + b\left( {a \ne 0} \right)\) + Đồ thị hàm số cắt trục hoành tại điểm có hoành độ bằng \( - 3\) thì tung độ bằng 0. + Thay tọa độ của điểm thuộc trục hoành và thuộc đồ thị hàm số vào hàm số để tìm 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 2 nên \(a = 2\) (thỏa mãn). Do đó, \(y = 2x + b\)Lại có, đường thẳng \(y = 2x + b\) cắt trục hoành tại điểm có hoành độ bằng \( - 3\) nên ta có:\(0 = 2.\left( { - 3} \right) + b\)\(b = 6\)Do đó, hàm số cần tìm là: \(y = 2x + 6\)

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