Final answer:
The equation of the line through (2, 6) parallel to y = 3x - 3.15 is y = 3x, as parallel lines have the same slope and the point-slope form leads us to the equation y = 3x through the given point.
Step-by-step explanation:
To find the equation of the line through (2, 6) that is parallel to the line given by y = 3x - 3.15, we first need to recognize that parallel lines have the same slope. The given line has a slope of 3, as seen by the coefficient of x. To find the new line's equation, we use the point-slope form which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
The point (2, 6) will be used for x1 and y1, and the slope m will be 3, the same as the slope of the original line. Thus, we substitute these values into the point-slope formula:
y - 6 = 3(x - 2)
We then distribute the 3 and add 6 to both sides to get:
y = 3x - 6 + 6
y = 3x
Finally, since we know the line has to pass through (2, 6), we can find the specific y-intercept (b) value by substituting the point's coordinates into the equation:
6 = 3(2) + b
b = 6 - 6
b = 0
So the correct equation of the parallel line through (2, 6) is:
y = 3x