The given line has equation
y = 3x + 4
The equation is in the slope-intercept form, y = mx + b,
where m = slope, and b = y-intercept.
This line has slope = m = 3.
Parallel lines have equal slopes, so the line we are looking for also has slope = 3.
The line will have an equation of the form
y = 3x + b
Now we need to find b, the y-intercept.
We use the given point in the equation we have so far to find b.
y = 3x + b
Using the given point, (3, 2), replace x with 3 and y with 2. Solve for b.
2 = 3(3) + b
2 = 9 + b
b = -7
Now we replace b with -7.
y = 3x + b
y = 3x - 7
Answer: The equation is y = 3x - 7