Final answer:
The equation of the line that is parallel to y = 3x and contains the point (4, 4) is y = 3x - 8.
Step-by-step explanation:
To find an equation for the line that is parallel to the line y = 3x and passes through the point (4, 4), we need to ensure that the slope of our new line is the same as the slope of the given line. The slope of the given line is 3, so our new line will also have a slope of 3.
The general form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept. Since we know the slope (m = 3) and a point on the line (4, 4), we can substitute these values into the equation and solve for b to find the y-intercept.
Substituting in we get: 4 = 3(4) + b, which simplifies to 4 = 12 + b. Solving for b, we find that b = -8. Therefore, the equation of the line is y = 3x - 8.