Question

Постройте график функции y= -4x+3 Укажите координаты точек пересечения графика с осями координат.

Answer 1

Graph of the Function y = -4x + 3

To plot the graph of the function y = -4x + 3, we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.

From the given equation, we can see that the slope (m) is -4 and the y-intercept (b) is 3. Therefore, the graph will have a slope of -4 and intersect the y-axis at the point (0, 3).

To find the x-intercept, we can set y = 0 and solve for x:

0 = -4x + 3 4x = 3 x = 3/4

So, the graph will intersect the x-axis at the point (3/4, 0).

Therefore, the coordinates of the points where the graph intersects the x and y axes are:

- X-intercept: (3/4, 0) - Y-intercept: (0, 3)

Graph of the Function y = -4x + 3:

import matplotlib.pyplot as plt
import numpy as np

x = np.linspace(-5, 5, 100)
y = -4*x + 3

plt.plot(x, y)
plt.xlabel('x')
plt.ylabel('y')
plt.title('Graph of y = -4x + 3')
plt.grid(True)
plt.axhline(0, color='black', linewidth=0.5)
plt.axvline(0, color='black', linewidth=0.5)
plt.scatter([3/4], [0], color='red', label='X-intercept: (3/4, 0)')
plt.scatter([0], [3], color='blue', label='Y-intercept: (0, 3)')
plt.legend()
plt.show()

The graph of the function y = -4x + 3 is a straight line with a slope of -4. It intersects the x-axis at the point (3/4, 0) and the y-axis at the point (0, 3).


Please note that the graph is a visual representation and the coordinates of the points of intersection may not be exact due to the limitations of the graphing software.