Final answer:
The slope of a line is determined by 'd. the change in the value of y divided by the change in the value of x', calculated as (y2 - y1)/(x2 - x1), known as 'rise over run'. Slope indicates how much y changes for every unit increase in x.
Step-by-step explanation:
The slope of a line is a numerical measurement of the line's steepness and is typically represented as the ratio of the change in the vertical (y) value to the change in the horizontal (x) value between two distinct points on the line. This ratio is often referred to as “rise over run.” When considering the question's options, the correct choice for the calculation of slope is 'd. the change in the value of y divided by the change in the value of x'. Mathematically, if we have two points, (x1, y1) and (x2, y2), the slope (m) would be calculated as (y2 - y1) divided by (x2 - x1).
For example, given a line with two points (2, 3) and (5, 9), the slope would be calculated by subtracting the y-values of the points (9 - 3 = 6) and dividing by the difference in the x-values (5 - 2 = 3), resulting in a slope of 2 or 6/3. This demonstrates that for every increase of one unit in x, y increases by two units on average.
The y-intercept is another essential characteristic of a linear equation, representing the point at which the line crosses the vertical y-axis. In the equation of a straight line, y = mx + b, m stands for the slope, and b is the y-intercept. Therefore, understanding the slope is crucial in graphing a line and analyzing the rate of change between variables.