Final answer:
The equation of the line that passes through the point (3,9) and is parallel to y=(4/5)x+7 is y=(4/5)x+33/5.
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 can be found using the slope-intercept form, y = mx + b. The slope of the given line is 4/5, which means any line parallel to it will have the same slope. So, the equation of the parallel line passing through the point (3,9) can be written as y = (4/5)x + b. We can substitute the coordinates of the point (3,9) into this equation to find the value of the y-intercept, b.
Substituting x = 3 and y = 9 into the equation y = (4/5)x + b:
9 = (4/5)(3) + b
9 = 12/5 + b
b = 9 - 12/5
b = 45/5 - 12/5
b = 33/5
So, the equation of the line that passes through the point (3,9) and is parallel to the line y = (4/5)x + 7 is y = (4/5)x + 33/5.