Question

1.Как с помощью графика линейной функции y=kx+m, где k(неравняется)0,решить. а)уравнение kx+m=0 б)неравенство kx+m>0 в)неравенство kx+m<(равно)0 2.В каком случае линейная функция возрастает а в каком убывает? Как об этом можно судить по графику линейной функции?

Answer 1

Рисуем график функции -  прямая.
1.
а) равно нулю - точка пересечения с осью Х.
k*x = - m
х = - m/k
б) больше нуля(но не равно 0) - все значения где график ВЫШЕ оси Х.
При k>0 получим
Х∈(-m/k;+∞)  - точка -m/k - НЕ ВХОДИТ - круглая скобка - на графике КРУГ(кольцо).
в) Ниже оси Х и равно 0.
Х∈(-∞; - m/k] - точка -m*k ВХОДИТ - квадратная скобка  - на графике -ТОЧКА.
2. Если коэффициент k больше 0 -  возрастает, меньше - убывает
Например, у = 2*х - возрастает, а у = - х - убывает

Answer 2

I will try to answer your questions in detail.

1. How to solve with the help of the graph of the linear function y = kx + m, where k ≠ 0, a) the equation kx + m = 0 b) the inequality kx + m > 0 c) the inequality kx + m ≤ 0

a) To solve the equation kx + m = 0, we need to find the value of x that makes y equal to zero. This means that we need to find the point where the graph of the linear function intersects the x-axis. The x-coordinate of this point is the solution of the equation. For example, if y = 2x - 4, then the graph intersects the x-axis at the point (2, 0), so the solution is x = 2.

b) To solve the inequality kx + m > 0, we need to find the values of x that make y positive. This means that we need to find the part of the graph of the linear function that is above the x-axis. The x-coordinates of this part are the solutions of the inequality. For example, if y = 2x - 4, then the graph is above the x-axis when x > 2, so the solution is x > 2.

c) To solve the inequality kx + m ≤ 0, we need to find the values of x that make y negative or zero. This means that we need to find the part of the graph of the linear function that is below or on the x-axis. The x-coordinates of this part are the solutions of the inequality. For example, if y = 2x - 4, then the graph is below or on the x-axis when x ≤ 2, so the solution is x ≤ 2.

2. In what case does the linear function increase and in what case does it decrease? How can this be judged by the graph of the linear function?

The linear function increases when the value of y increases as the value of x increases. This means that the graph of the linear function has a positive slope, or the angle of inclination is acute. The value of the slope is equal to the coefficient k in the equation y = kx + b. For example, if y = 2x - 4, then the graph has a positive slope of 2 and the function increases.

The linear function decreases when the value of y decreases as the value of x increases. This means that the graph of the linear function has a negative slope, or the angle of inclination is obtuse. The value of the slope is equal to the coefficient k in the equation y = kx + b. For example, if y = -x + 3, then the graph has a negative slope of -1 and the function decreases.

You can find more information about the linear function and its graph in the following sources: [График линейной функции. Свойства и Формулы](https://skysmart.ru/articles/mathematic/grafik-linejnoj-funkcii), [Линейная функция y = kx + b Flashcards | Quizlet](https://quizlet.com/606872163/%D0%9B%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D0%B0%D1%8F-%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F-y-kx-b-flash-cards/), [\"Функция y=kx, ее свойства и график\"](https://infourok.ru/funkciya-y-kx-ee-svojstva-i-grafik-5571042.html). I hope this helps you.