Final answer:
The equation of the line parallel to y = (3/5)x - 1 passing through the point (1,9) is y = (3/5)x + 42/5.
Step-by-step explanation:
The student is asking for the equation of a line parallel to the given line y = (3/5)x - 1 and passing through the point (1,9). To find this, we need to use the concept that parallel lines have the same slope. Given that the slope (m) of the initial line is 3/5, our new line will have the same slope. We then utilize the point-slope form of a line equation, which is y - y1 = m(x - x1), where (x1, y1) is the point the line passes through.
Substituting the point (1, 9) and the slope 3/5 into the point-slope form, we get:
y - 9 = (3/5)(x - 1).
Expanding this, we get:
y - 9 = (3/5)x - (3/5).
To put this in slope-intercept form, we add 9 to both sides, obtaining:
y = (3/5)x + 9 - (3/5).
Combining like terms:
y = (3/5)x + (45/5) - (3/5).
Simplifying this, we get:
y = (3/5)x + 42/5.
This is the equation of the line parallel to y = (3/5)x - 1 and goes through the point (1, 9).