Final answer:
The equation of the line parallel to -3y = -6x + 1 that passes through the point (9,0) is y = 2x - 18. This is obtained by finding the slope of the given line and applying it to the slope-intercept form with the new point to solve for the y-intercept.
Step-by-step explanation:
To find the equation of the line parallel to -3y = -6x + 1 and passing through the point (9,0), we start by writing the given equation in slope-intercept form.
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. Dividing the given equation by -3, we get y = 2x - \(\frac{1}{3}\).
This tells us that the slope of the parallel line must also be 2 since parallel lines have the same slope.
To find the y-intercept of the new line, we use the point it passes through, (9,0).
Plugging the coordinates into the slope-intercept equation, we get: 0 = 2(9) + b.
Solving for b yields b = -18.
Therefore, the equation of the line parallel to the given line and passing through (9,0) is y = 2x - 18.