Final answer:
To find a line parallel to y = 3x + 5 and going through the point (3, 2), we use the point-slope form of a line. The equation of the parallel line is y = 3x - 7.
Step-by-step explanation:
To find a line that is parallel to the line y = 3x + 5 and goes through the point (3, 2), we need to find a line with the same slope. The slope of the given line is 3. So, the equation of the new line will also have a slope of 3. Using the point-slope form of a line, y - y1 = m(x - x1), we substitute the values m = 3, x1 = 3, and y1 = 2 to find the equation of the parallel line:
y - 2 = 3(x - 3)
Simplifying the equation:
y - 2 = 3x - 9
y = 3x - 7
Therefore, the line parallel to y = 3x + 5 and passing through the point (3, 2) is y = 3x - 7.