Question

Постройте график функции y=2x-3y

Answer 1

Y + 3y = 2x
4y = 2x
y = 2/4*x
y = 1/2*x 

см скриншот
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Answer 2

To plot the graph of the equation y = 2x - 3y, we first need to rearrange the equation to the standard form, which is y = f(x). Let's do that:

y = 2x - 3y

Add 3y to both sides: 4y = 2x

Divide both sides by 4: y = (2/4)x

Simplify: y = (1/2)x

Now we have the equation in the form y = f(x), where f(x) = (1/2)x. This equation represents a straight line with a slope of 1/2 and a y-intercept of 0.

Let's plot the graph:

1. Choose a range of x-values (e.g., from -5 to 5).
2. Calculate corresponding y-values using the equation y = (1/2)x.
3. Plot the points (x, y) on the graph.
4. Draw a straight line passing through these points.

Here is the graph:

luaCopy code
  |                   *
  |                 *   
  |               *     
  |             *       
  |           *         
  |         *           
  |       *             
  |     *               
  |   *                 
  | *                   
  -----------------------

Keep in mind that the slope of 1/2 means that for every 2 units of x, the corresponding y-value increases by 1 unit. The line passes through the origin (0, 0). The graph is a straight line with a positive slope.