Final answer:
The equation of the line that is parallel to the given line and has an x-intercept of -3 is y = 0. Therefore, the equation of the line that is parallel to the given line and has an x-intercept of -3 is y = 0.
Step-by-step explanation:
The equation of a line that is parallel to the given line and has an x-intercept of -3 can be determined using the slope-intercept form of a linear equation, which is y = mx + b. In this form, 'm' represents the slope of the line and 'b' represents the y-intercept.
Given that the original line has a slope of 3 and a y-intercept of 9 (as represented by the equation y = 9 + 3x), we can conclude that any line parallel to it will also have a slope of 3.
Since the x-intercept is -3, we can substitute this value for 'x' and solve for 'y'.
Substituting -3 for 'x' in the equation y = 9 + 3x, we get y = 9 + 3(-3), which simplifies to y = 9 - 9 = 0.
Therefore, the equation of the line that is parallel to the given line and has an x-intercept of -3 is y = 0.