Final answer:
The equation of a line in slope-intercept form with a slope of 3 and a y-intercept of 9 is y = 3x + 9. This form illustrates the characteristics of the line, with the slope value determining the steepness and the y-intercept indicating where the line crosses the y-axis.
Step-by-step explanation:
The question involves writing the equation of a straight line in slope-intercept form, which is commonly represented as y = mx + b, where m is the slope of the line and b is the y-intercept. Given that the slope (m) is 3 and the y-intercept (b) is 9 from Figure A1, the equation of the line can be written as y = 3x + 9. This equation reflects a line that will rise by 3 units on the y-axis for every single unit it moves along the x-axis, and it crosses the y-axis at the point (0,9).
In the context of this figure and the explanation provided, the b and m terms in the equation determine the shape of the line graphed on the Cartesian plane. The higher the absolute value of the slope, the steeper the line, and the y-intercept indicates the point at which the line crosses the y-axis. Understanding these concepts is critical when working with linear equations and graphing lines.