Тренажер. Линейная функция. Постройте графики функций (каждый на отдельных КП), для каждого из них выпишите значения коэффициентов к и в. Задание выполнить в тетради. 1) y = 2x - 2; 2) y = 2x + 2; 3) y = 3x-1; 4) y = 3x + 4; 5) y = 2 + x; 6) y = -2-x; 7) y = - 2x + 1; 8) y = 5 - x; 9) y = 3 + x; 10) y = -3 + x; 11) y=-x-3; 12) y = - 2x - 5; 13) y = 3x + 2; 14) y = 3x + 4; 15) y = - 2 + 4x; 16) y = 0,5x-2; 17) y = 0,5x + 2; 18) y = 0,5x-5; 19) y = - 0,5x + 4; 20) y = 1 - 5x; 1 1 21) y = 3 x - 1; 22) y = 3 x + 3; 1 1 23) y = - 3x-2; 24) y = -3 x + 1; X 1 5 25) y = 2-2; 26) y=3x-2; = 1 27) y = 4x + 2; 29) y 28) y = 4 - 1; X = 5 + 4; 30) y = -1 +6.

Решение:

Линейная функция имеет вид $$y = kx + b$$, где k и b - коэффициенты.

1. $$y = 2x - 2$$, $$k = 2$$, $$b = -2$$
2. $$y = 2x + 2$$, $$k = 2$$, $$b = 2$$
3. $$y = 3x - 1$$, $$k = 3$$, $$b = -1$$
4. $$y = 3x + 4$$, $$k = 3$$, $$b = 4$$
5. $$y = 2 + x = x + 2$$, $$k = 1$$, $$b = 2$$
6. $$y = -2 - x = -x - 2$$, $$k = -1$$, $$b = -2$$
7. $$y = -2x + 1$$, $$k = -2$$, $$b = 1$$
8. $$y = 5 - x = -x + 5$$, $$k = -1$$, $$b = 5$$
9. $$y = 3 + x = x + 3$$, $$k = 1$$, $$b = 3$$
10. $$y = -3 + x = x - 3$$, $$k = 1$$, $$b = -3$$
11. $$y = -x - 3$$, $$k = -1$$, $$b = -3$$
12. $$y = -2x - 5$$, $$k = -2$$, $$b = -5$$
13. $$y = -3x + 2$$, $$k = -3$$, $$b = 2$$
14. $$y = -3x + 4$$, $$k = -3$$, $$b = 4$$
15. $$y = -2 + 4x = 4x - 2$$, $$k = 4$$, $$b = -2$$
16. $$y = 0.5x - 2$$, $$k = 0.5$$, $$b = -2$$
17. $$y = 0.5x + 2$$, $$k = 0.5$$, $$b = 2$$
18. $$y = 0.5x - 5$$, $$k = 0.5$$, $$b = -5$$
19. $$y = -0.5x + 4$$, $$k = -0.5$$, $$b = 4$$
20. $$y = 1 - 5x = -5x + 1$$, $$k = -5$$, $$b = 1$$
21. $$y = \frac{1}{3}x - 1$$, $$k = \frac{1}{3}$$, $$b = -1$$
22. $$y = \frac{1}{3}x + 3$$, $$k = \frac{1}{3}$$, $$b = 3$$
23. $$y = -\frac{1}{3}x - 2$$, $$k = -\frac{1}{3}$$, $$b = -2$$
24. $$y = -\frac{1}{3}x + 1$$, $$k = -\frac{1}{3}$$, $$b = 1$$
25. $$y = 2 - \frac{x}{5} = -\frac{1}{5}x + 2$$, $$k = -\frac{1}{5}$$, $$b = 2$$
26. $$y = \frac{1}{5}x - 2$$, $$k = \frac{1}{5}$$, $$b = -2$$
27. $$y = -\frac{1}{4}x + 2$$, $$k = -\frac{1}{4}$$, $$b = 2$$
28. $$y = \frac{x}{4} - 1 = \frac{1}{4}x - 1$$, $$k = \frac{1}{4}$$, $$b = -1$$
29. $$y = \frac{x}{5} + 4 = \frac{1}{5}x + 4$$, $$k = \frac{1}{5}$$, $$b = 4$$
30. $$y = -1 + \frac{x}{6} = \frac{1}{6}x - 1$$, $$k = \frac{1}{6}$$, $$b = -1$$

Ответ: см. решение