The task is to analyze the image and extract relevant information. The image contains a math problem. The student's name is "Юпатов Артём". The problem number is "№4". The equation to be graphed is "y = -x". There is a table with columns for 'x' and 'y' to fill in coordinates. A coordinate plane is provided for graphing.
To solve this problem, we need to:
1. Choose some values for 'x'.
2. Calculate the corresponding 'y' values using the equation y = -x.
3. Plot these (x, y) points on the coordinate plane.
4. Draw a line through the points, which will be the graph of the equation y = -x.
Let's fill in the table and then consider graphing it.
| x | y |
|---|---|
| 0 | 0 |
| 1 | -1 |
| -1 | 1 |
| 2 | -2 |
| -2 | 2 |
Now, let's describe the graphing process:
1. Plotting Points:
* Point 1: (0, 0) - This is the origin.
* Point 2: (1, -1) - Move 1 unit to the right on the x-axis and 1 unit down on the y-axis.
* Point 3: (-1, 1) - Move 1 unit to the left on the x-axis and 1 unit up on the y-axis.
* Point 4: (2, -2) - Move 2 units to the right on the x-axis and 2 units down on the y-axis.
* Point 5: (-2, 2) - Move 2 units to the left on the x-axis and 2 units up on the y-axis.
2. Drawing the Line:
Since this is a linear equation (y = -x), the graph will be a straight line. Connect the plotted points with a straight line. This line will pass through the origin (0,0) and will be in the second and fourth quadrants, sloping downwards from left to right.
This equation represents a direct proportionality where y is always the negative of x. The graph is a straight line passing through the origin with a slope of -1.