Final answer:
To find the equation of a line parallel to y = (4/5)x + 7 and passing through the point (3, 9), we use the point-slope form of a linear equation and determine the slope is 4/5. The equation of the parallel line is y = (4/5)x - 11.
Step-by-step explanation:
The equation of the line that passes through the point (3, 9) and is parallel to the line y = (4/5)x + 7 must have the same slope, which is 4/5. To find the equation of our line, we use the point-slope form, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Given the point (3, 9), we plug in the values to get y - 9 = (4/5)(x - 3). Simplifying, we get y = (4/5)x + (4/5)*3 + 9 - (4/5)*3, which simplifies further to y = (4/5)x + 9 - 12/5 = (4/5)x + 45/5 - 12/5, which gives us y = (4/5)x + 33/5. Therefore, the equation in y-intercept form is y = (4/5)x - 11, which corresponds to option (b).