A line has a y-intercept of 5 and is parallel to the line represented by the equation 2x + 3y = 9. Which of the following equations represents the line?

First, we need to find the slope of the given line. The equation of the line is in the form of Ax + By = C. We can convert it to the slope-intercept form (y = mx + b) to easily find the slope.

The given equation is 2x + 3y = 9. Let's isolate y:

3y = -2x + 9 y = (-2/3)x + 3

So, the slope (m) of the given line is -2/3.

Since parallel lines have the same slope, the line we're looking for also has a slope of -2/3.

We're also told that the y-intercept (b) of the line we're looking for is 5.

So, the equation of the line we're looking for, in slope-intercept form, is:

y = (-2/3)x + 5