Final answer:
The first number in a slope ratio represents the horizontal change or 'run', while the second number represents the vertical change or 'rise'. The calculation of slope as 'rise over run' is essential in determining the direction and steepness of a line on a graph.
Step-by-step explanation:
When given a slope ratio, the first number represents the horizontal change, often referred to as the 'run', and the second number represents the vertical change, or 'rise'. In the context of a slope ratio, such as one might find on a graph of a straight line, the slope (m) is computed as the rise over run. This is a way of quantifying how steep a line is. For instance, if a line on a graph goes up 2 units for every 3 units it goes to the right, the slope would be ⅓ or simply '2 over 3'. Slope is a fundamental concept in algebra and coordinate geometry that describes the direction and the steepness of a line.
The slope formula, which is the 'rise' (difference in y-values) divided by the 'run' (difference in x-values) between two points, gives a ratio that represents the slope of the line. If we consider an example involving a physics concept such as voltage and current, and we have a graph where a line rises by 1 mA (0.001 A) for every 1 V of run, then the slope would be 1 mA/V. Similarly, if you were to calculate the slope of an air density graph between altitudes of 4,000 meters and 6,000 meters, you would designate a starting point and an ending point and use the rise over run between them to find the slope, which might be expressed in numerical terms like '2.89'.