Final answer:
The point-slope form is advantageous when the specific point and slope are known, while slope-intercept form is best when emphasizing the y-intercept. The slope indicates the direction and steepness of the line, with positive, negative, and zero slopes corresponding to increasing, decreasing, and flat lines, respectively.
Step-by-step explanation:
The preference between point-slope form and slope-intercept form often depends on the information available and the specific application. Point-slope form is often considered more useful than slope-intercept form when you have a point on the line and the slope but do not necessarily have the y-intercept. Point-slope form is: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point on the line. It is especially helpful when finding the equation of a line that passes through a specific point.
On the other hand, the slope-intercept form is given as y = mx + b, where m is the slope and b is the y-intercept. This form quickly shows where the line crosses the y-axis, which can also be valuable depending on what you need to find or illustrate.
Regarding the slope, a positive slope indicates that as x increases, y also increases, while a negative slope means that as x increases, y decreases. A zero slope indicates that y does not change as x changes, resulting in a horizontal line. The slope is crucial in many fields, such as economics, to illustrate the relationship between two variables.