Final answer:
The slope of a straight line between two data points reflects the rate of change between the variables represented on the axes. To calculate the slope, find the difference in y-values (rise) and x-values (run) between two points and divide rise by run. For example, a line representing air density at different altitudes between 4,000 and 6,000 meters has a slope of -0.207 per 2,000 meters.
Step-by-step explanation:
The slope of a straight line can be understood as the rate at which one variable changes with respect to another. It is represented numerically as the change in the y-value (rise) divided by the change in the x-value (run). Since the slope is constant along any straight line, selecting two points on the line allows us to calculate the slope. For instance, if we evaluate the slope at points representing an altitude of 4,000 meters and 6,000 meters, we can find the slope related to the air density over this distance.
To compute the slope, we take the change in air density (rise) which is 0.100 - (-0.307) giving us -0.207. Then we take the change in altitude (run) as 6,000 - 4,000 which is 2,000 meters. The slope is therefore -0.207 per 2,000 meters. Essentially, this suggests that from the altitude of 4,000 meters up to 6,000 meters, the density of the air decreases by approximately 0.1 kilograms/cubic meter for every 1,000 meters increase in altitude.
In a more general sense, when considering a graph with an x-axis and a y-axis, the slope can also be visually determined if the line is straight and the y-intercept and slope value are known. For example, according to FIGURE A1, the slope of a line that crosses the y-axis at 9 (y-intercept) and has a rise of 3 for every 1 increase on the horizontal axis is exactly 3. This tells us how steeply a line ascends or descends over the plane.