Final answer:
The slope of a line graph is the ratio of the rise over the run between any two points on the line. A line with a slope of 3 rises 3 units for every 1 unit it runs horizontally. To calculate the slope numerically, use the formula (y2 - y1) / (x2 - x1) with coordinates of two points.
Step-by-step explanation:
Calculating the slope of a line on a graph is a fundamental concept in algebra and coordinate geometry, critical for high school students to understand. The slope is a measure of the steepness of a line and is calculated as the ratio of the rise (change in y) over the run (change in x) between two points on the line. Based on the provided information, FIGURE A1 presents a line graph with a y-intercept of 9 and a slope of 3. This indicates that for every 1 unit increase in the x-axis (horizontal axis), there is a 3 unit increase in the y-axis (vertical axis).
To calculate the slope numerically, consider two points on the line graph. For instance, if we were looking at an air density graph and were interested in calculating the slope between the points representing an altitude of 4,000 meters and an altitude of 6,000 meters, we would identify the y-values corresponding to these x-values, then use the formula slope = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.