Question

Не выполняя построение графика функции y=2x-7, найдите координаты точки этого графика, у которой 2) абсцисса и ордината-противоположные числа

Answer 1

y=2x-7,
у=-х

-х=2х-7
-3х=-7
х=7/3

х=2_1/3
у=-2_1/3

(2_1/3; -2_1/3) - точка графика, координаты которой противоположны.

Answer 2

Finding the Coordinates of a Point on the Graph of y = 2x - 7

To find the coordinates of a point on the graph of the function y = 2x - 7, where the x-coordinate and y-coordinate are opposite numbers, we can set up an equation and solve for x.

Let's assume that the x-coordinate is represented by the variable 'a'. Since the x-coordinate and y-coordinate are opposite numbers, the y-coordinate can be represented by '-a'.

Substituting these values into the equation y = 2x - 7, we get:

-a = 2a - 7

Simplifying the equation, we have:

3a = 7

Dividing both sides of the equation by 3, we find:

a = 7/3

Therefore, the x-coordinate of the point is 7/3, and the y-coordinate is -7/3.

So, the coordinates of the point on the graph of y = 2x - 7, where the x-coordinate and y-coordinate are opposite numbers, are (7/3, -7/3).