Question

В одній системі координат побудуйте графіки функцій у = - 3x i y = 6 . Запишіть координати їх перетину.​

Answer 1

Ответ:

А (-2; 6)

Объяснение:

у= -3х      х=0;  у=0,   х=2;  у=-6

у=6        

Answer 2

Plotting the Functions

To plot the functions u = -3x + i and y = 6, we can use a Cartesian coordinate system. The first function represents a straight line with a slope of -3 and a y-intercept of 1. The second function is a horizontal line at y = 6.

Let's plot these functions on a graph:

import matplotlib.pyplot as plt
import numpy as np

x = np.linspace(-10, 10, 100)  # Generate 100 x-values from -10 to 10
u = -3 * x + 1  # Calculate the corresponding y-values for the first function
y = np.full_like(x, 6)  # Create an array of y-values equal to 6

plt.plot(x, u, label='u = -3x + 1')
plt.plot(x, y, label='y = 6')
plt.xlabel('x')
plt.ylabel('y')
plt.title('Graph of u = -3x + 1 and y = 6')
plt.legend()
plt.grid(True)
plt.show()

The graph will show the two functions intersecting at a specific point.

Finding the Intersection Coordinates

To find the coordinates of the intersection point, we need to solve the system of equations formed by the two functions. In this case, we have:

u = -3x + 1
y = 6

To find the intersection point, we can set the two equations equal to each other:

-3x + 1 = 6

Solving this equation will give us the x-coordinate of the intersection point. Let's solve it:

-3x + 1 = 6
-3x = 6 - 1
-3x = 5
x = 5 / -3
x = -5/3

Now that we have the x-coordinate, we can substitute it back into either of the original equations to find the y-coordinate. Let's use the equation u = -3x + 1:

u = -3(-5/3) + 1
u = 5 + 1
u = 6

Therefore, the coordinates of the intersection point are (-5/3, 6).

Please note that the specific details of the sources you provided were not available. However, the information provided above is based on general mathematical principles and should be accurate.