Final answer:
To find an equation of a line that passes through a given point and is parallel to another line, we need to use the fact that parallel lines have the same slope. The equation of the line that passes through the point (6,3) and is parallel to the line 5x-3y=9 is y - 3 = (5/3)(x - 6).
Step-by-step explanation:
To find an equation of a line that passes through a given point and is parallel to another line, we need to use the fact that parallel lines have the same slope. The given line has the equation 5x-3y=9. To find its slope, we need to rearrange the equation to the form y = mx + b, where m is the slope. So, 5x-3y = 9 becomes -3y = -5x + 9, which simplifies to y = (5/3)x - 3. Therefore, the slope of the given line is 5/3.
Since the line we are looking for is parallel to the given line, it will also have a slope of 5/3. We also know that the line passes through the point (6,3). Using the point-slope form of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line, we can substitute the values into the equation.
With the slope of 5/3 and the point (6,3), the equation of the line that passes through the point (6,3) and is parallel to the line 5x-3y=9 is: y - 3 = (5/3)(x - 6).