To determine how many times larger the slope of the blue line is in comparison to the black line, you will need to calculate the ratio of the slopes.
Here are the steps we need to take in order to find this ratio:
1. Determine the slopes of the two lines. The slope of a line is calculated by finding the difference in the vertical coordinates (often represented as y) and dividing it by the difference in the horizontal coordinates (often represented as x). We will refer to the slope of the blue line as 'blue_slope' and the slope of the black line as 'black_slope'.
2. Once we have found these slopes, we can then calculate the ratio. This is done by dividing the slope of the blue line (blue_slope) by the slope of the black line (black_slope).
3. This calculation will give us the ratio of the slopes, telling us how many times larger the slope of the blue line is compared to the black line. If the ratio is greater than 1, this means that the slope of the blue line is greater than the slope of the black line. If the ratio is less than 1, the slope of the black line is greater.
To summarize, the ratio of the slopes is calculated by dividing the slope of the blue line by the slope of the black line. This will tell us how many times larger the slope of one line is in comparison to the other.