Final answer:
To find the equation of the line parallel to the given line 5x-3y=9 and passing through the point (-6,-3), you need to determine the slope of the given line and use it in the point-slope form of a line to find the equation.
Step-by-step explanation:
To find the equation of a line that is parallel to the given line, we need to determine the slope of the given line. The slope of the given line can be found by rearranging the equation into slope-intercept form: y = (5/3)x - 3. The slope of the line is the coefficient of x, which in this case is 5/3.
Since the line we're looking for is parallel to the given line, it will have the same slope. So the slope of the new line is also 5/3. We can then use the point-slope form of a line, y - y1 = m(x - x1), and plug in the coordinates of the given point (-6,-3) and the slope to find the equation. Plugging in the values, we get: y + 3 = (5/3)(x + 6). Simplifying further, the equation becomes y = (5/3)x + 11. Therefore, the equation of the line parallel to 5x - 3y = 9 and passing through the point (-6,-3) is y = (5/3)x + 11.