Find the slope of the line and describe how the y-coordinate changes in relation to the x-coordinate.

To find the slope of a line, you need two points on the line. Let's call the coordinates of the first point (x1, y1) and the coordinates of the second point (x2, y2).

The slope of a line is given by the formula:

slope = (y2 - y1) / (x2 - x1)

Now, let's say that the y-coordinate increases as the x-coordinate increases. In this case, the line would have a positive slope. This means that as you move from left to right along the line, the y-coordinate will also increase.

Conversely, if the y-coordinate decreases as the x-coordinate increases, the line would have a negative slope. In this case, as you move from left to right along the line, the y-coordinate will decrease.

If the line is horizontal (parallel to the x-axis), then the slope is zero, and the y-coordinate remains constant regardless of the change in the x-coordinate.

Finally, if the line is vertical (parallel to the y-axis), the slope is undefined, as there is no change in the x-coordinate.

So, to conclude, the slope of a line tells you the rate at which the y-coordinate changes in relation to the x-coordinate. A positive slope means the y-coordinate increases as the x-coordinate increases, a negative slope means the y-coordinate decreases as the x-coordinate increases, a slope of zero means the y-coordinate remains constant, and an undefined slope means there is no change in the x-coordinate.

To find the slope of a line, we need two points on the line. Let's denote these two points as (x₁, y₁) and (x₂, y₂). The slope (m) of the line is given by the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Now, let's analyze how the y-coordinate changes in relation to the x-coordinate based on the value of the slope:

1. If the slope (m) is positive (+), it means that as the x-coordinate increases, the y-coordinate also increases. This indicates a positive correlation between x and y.

2. If the slope (m) is negative (-), it means that as the x-coordinate increases, the y-coordinate decreases. This indicates a negative correlation between x and y.

3. If the slope (m) is zero (0), it means that the y-coordinate remains constant as the x-coordinate changes. This indicates no correlation between x and y.

4. If the slope (m) is undefined, it means that the line is vertical, and there is no change in the y-coordinate as the x-coordinate changes.

Hope this helps! Let me know if you have any further questions.