Find the equation of the line in slope intercept form that is perpendicular to y-9=-1/2(x-2) and passes through (0,4)

The slopes of perpendicular lines are called negative reciprocals of each other. You may have heard of this as negative opposites. Basically, if you have one line with a slope of 3/4, then a line perpendicular to it would have a slope of -4/3.
The original equation they give you is in point-slope form: y-y1=m(x-x1) with 1/2 being the slope of the line.
If the slope of the original line is 1/2, then the slope of the line perpendicular to that would be -2/1 or just -2.
The problem also gives you the y-int. (0,4).
Now you have all the information needed to put it in slope intercept form.
slope intercept form is y=mx+b where m is slope and b is the value of the y intercept. 
From previous calculations we know that the slope of our line is -2 and the y-intercept is 4.
Substitute in those values: y=-2x+4
that's you )

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