Final answer:
The equation of the line passing through the point (4,-1) and parallel to y = 3x is y = 3x - 13, maintaining the same slope of 3.
Step-by-step explanation:
The question asks us to find the equation of a line that passes through the point (4,-1) and is parallel to the equation y = 3x. Since parallel lines have the same slope, our new line will also have a slope of 3. To find the y-intercept (b) of our new line, we use the point-slope form of the equation y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point.
Plugging in the given point (4, -1) and the slope 3, we get y + 1 = 3(x - 4). Expanding the equation, we have y + 1 = 3x - 12. To get the equation in slope-intercept form (y = mx + b), we subtract 1 from both sides to find y = 3x - 13 as our final equation.
Therefore, the equation of the line that passes through the point (4,-1) and is parallel to y = 3x is y = 3x - 13.