Final answer:
Point-slope form is used when the slope and a specific point on the line are known because it is more versatile and intuitive for writing the line's equation, especially when the point is not the y-intercept.
Step-by-step explanation:
When you have the slope of a line and a point that the line passes through, it's often useful to use the point-slope form of the line's equation, especially if the point is not the y-intercept. One might prefer the point-slope form over the slope-intercept form for its versatility. The point-slope form can easily accommodate any point on the line and is a direct expression of the slope definition, which is change in y over change in x. This makes it quite intuitive to write the equation of a line when you're given a point and a slope.
For example, given a slope (m) of 3 and a point (x1, y1) = (2, 6), the point-slope form of the equation is y - y1 = m(x - x1), which would yield y - 6 = 3(x - 2). This form immediately shows how moving away from the point (2, 6) will change the value of y based on the slope. On the other hand, slope-intercept form (y = mx + b) requires solving for the y-intercept b, which may not be as straightforward when the given point is not the y-intercept.