Final answer:
The slope-intercept form of the line with a slope of 3 and a y-intercept of 9 is y = 3x + 9. The point-slope form is y - 9 = 3x, based on the point (0, 9) which is on the line.
Step-by-step explanation:
To write the equation of the line in slope-intercept form, which is y = mx + b, we first identify the slope (m) and the y-intercept (b). According to the information provided, the slope of the line is 3, and the y-intercept is 9. Thus, the slope-intercept form of the equation would be y = 3x + 9.
The point-slope form of the equation is y - y1 = m(x - x1), where (x1, y1) is any point on the line and m is the slope. Since we know the y-intercept is at the point (0, 9), we can write the point-slope form as y - 9 = 3(x - 0), or simply y - 9 = 3x.
The slope and y-intercept of a linear equation are key components that determine the line's shape and position on a graph, and these principles are essential no matter which form of the equation we use.