Final answer:
To find the equation of a line parallel to y=3x that passes through (3,5), we maintain the same slope of 3 and use the point-slope form to get the equation y = 3x - 4.
Step-by-step explanation:
The question asks for the equation of a line that is parallel to the line represented by y=3x and that passes through the points (3,5) and (4,8). To find the equation of such a line, we first need to ensure it has the same slope as the line it is parallel to.
The original line y=3x has a slope of 3. Since parallel lines have the same slope, our new line will also have a slope of 3. Using the point-slope form y - y1 = m(x - x1), with m being the slope and (x1,y1) being a point the line passes through, we can substitute one of our given points, for example, (3,5). This gives us the equation y - 5 = 3(x - 3).
Expanding this equation and solving for y gives us y - 5 = 3x - 9, and adding 5 to both sides gives us the final equation of the line, which is y = 3x - 4.