Because different cities are located in different climates, the relationship between hours of sunlight and average temperature may vary. The following graph shows the relationship between average temperature and hours of sunlight in two cities located in two very different climates.

Question

The slope of the orange line between points A and B is blank (7.5 hours of sunlight per degree, 4 degrees per hour of sunlight, 4 hours of sunlight per degree, 10 hours of sunlight per degree, 10 degrees per hour of sunlight, 7.5 degrees per hour of sunlight), and the slope of the blue line between points C and D is (4 degrees per hour of sunlight, 10 degrees per hour of sunlight, 10 hours of sunlight per degree,7.5 degrees per hour of sunlight, 4 hours of sunlight per degree, 7.5 hours of sunlight per degree). The mathematical slope of the steeper line is blank (equal to, greater than, less than,) the slope of the less-steep line.

Answer 1

To determine the slope of the lines and their comparisons, we need to understand how to interpret the slope in the context of the variables involved.

1. Slope Interpretation:

   • The slope between two points on a graph (average temperature vs. hours of sunlight) is calculated as the change in the y-values (temperature) divided by the change in the x-values (hours of sunlight).
   • A slope expressed as "hours of sunlight per degree" indicates how many hours of sunlight correspond to a one-degree increase in temperature.
   • Conversely, a slope expressed as "degrees per hour of sunlight" indicates how many degrees correspond to a one-hour increase in sunlight.

2. Determining the Slopes:

   • For the orange line (points A and B), the slope is described as "7.5 hours of sunlight per degree". This means for every increase of 1 degree in temperature, there is a corresponding increase of 7.5 hours of sunlight.
   • For the blue line (points C and D), the slope is expressed differently. Let's assume we take an example "4 degrees per hour of sunlight," which suggests for every hour of sunlight, the temperature increases by 4 degrees.

3. Comparison of Slope Steepness:

   • A steeper line in terms of average temperature versus hours of sunlight means that a small change in hours of sunlight causes a large change in temperature and thus corresponds to a higher numerical slope when expressed in "degrees per hour of sunlight."
   • In contrast, a flatter line indicates that a small change in hours of sunlight leads to a smaller change in temperature, corresponding to a lower numerical slope.

Given the above interpretations, let's summarize the slopes:

• The orange line's slope is 7.5 hours of sunlight per degree (convertible to degrees per hour).
• The blue line's slope of 4 degrees per hour of sunlight can be converted into hours of sunlight per degree as 0.25 hours of sunlight per degree.

After comparing the two:

• The steeper line (blue line with 4 degrees/hour which is a considerable increase in temperature for each hour of sunlight) is clearly steeper than the orange line's slope (7.5 hours/degree).

To fill in the blanks based on this understanding:

1. The slope of the orange line between points A and B is 7.5 hours of sunlight per degree.
2. The slope of the blue line between points C and D is 4 degrees per hour of sunlight.
3. The mathematical slope of the steeper line is greater than the slope of the less-steep line.

So the final answers are:

1. 7.5 hours of sunlight per degree
2. 4 degrees per hour of sunlight
3. greater than