Final answer:
To find the equation of a line parallel to y = 5x + 3 passing through (6, 3), first note that parallel lines have the same slope. Using the slope 5 and the given point, we determine the y-intercept by plugging them into the point-slope formula, which yields y = 5x - 27.
Step-by-step explanation:
The student has asked for an equation of a line that is parallel to the line y = 5x + 3 and passes through the point (6, 3). Lines that are parallel have the same slope. Therefore, the slope of the new line will also be 5, the same as the given line. To find the y-intercept (b) of the new line, we use the point-slope form of a line equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through.
Using the point (6, 3) and the slope 5, the equation becomes:
3 = 5(6) + b. Simplifying this gives us 3 = 30 + b, and solving for b gives us b = -27. Therefore, the equation of the new line is y = 5x - 27.