Answer
$y=3x+4$
Work Step by Step
RECALL:
(1) The point-slope form of a line's equation is $y-y_1=m(x-x_1)$ where $m$=slope and $(x_1, y_1)$ is a point on the line.
(2) The slope-intercept form of a line's equation is $y=mx+b$ where $m$=slope and $b$ is the y-coordinate of the line's y-intercept.
(3) Parallel lines have equal slopes.
(4) Perpendicular lines have slopes whose product is $-1$.
The line is parallel to $y=3x+7$. Since the slope of this line is $3$, then the slope of the line parallel to it is also $3$.
Using the given point on the line $(0, 4)$ (which is the y-intercept) and the slope $3$, the equation of the line in slope-intercept form is:
$y=3x+4$
