Final answer:
The equation of the line 9x + 12y = -108 is converted to the slope-intercept form by isolating y, leading to the equation y = -3/4x - 9. Therefore, the correct answer is b. y = -3/4x - 9.
Step-by-step explanation:
The task at hand is to convert the equation of a line, 9x + 12y = -108, into slope-intercept form, which can be written as y = mx + b where m represents the slope and b represents the y-intercept. The slope-intercept form is useful because it clearly shows both of these characteristics for the line.
To start, we need to isolate y on one side of the equation. We'll do this by first subtracting 9x from both sides to get 12y = -9x - 108. Next, to solve for y, we divide every term by 12, leading to y = -3/4x - 9. This new equation shows us that the slope of the line is -3/4, and the y-intercept is at -9. Therefore, the correct response to the question is b. y = -3/4x - 9.
It's important to note that the information provided in the reference, which states a line with an equation y = 9 + 3x, is not directly relevant to this question. There appears to be an error in the reference materials since the line described would have a slope of 3 and a y-intercept of 9, and none of the answer choices correspond to this line.