Answer:
f(x) = 3x - 6
Explanation:
The equation of a line in slope-intercept form is y = mx + b where m = slope and b = y-intercept(the point where the line crosses the y-axis)
Parallel lines have the same slope
The slope of the given line is y = 3x - 2
So the slope of this line is 3 and the y intercept is -2
A parallel line will have the same slope of 3 but its y intercept will be different
Therefore a line parallel to 3x -2 will be of the form
y = 3x + b where b is the y-intercept of this parallel lne
To compute b, plug in values of y and x for the point (4, 6) through which the line passes ie at x = 4 and y = 6
This gives
6 = 3(4) + b
6 = 12 + b
Subtract 12 from both side:
6 - 12 = 12 - 12 + b
-6 = b
same as b = -6
Equation of parallel line is
y = 3x - 6
or
f(x) = 3x - 6