Question 366334
I don't know that I can show you a "formula" but I can show you a procedure.
You want your answer to be an equation in the slope-intercept form:
{{{y = mx+b}}} of a line that is perpendicular to the line {{{y = 2x-4}}} and which passes through the point (4, 7).
Let's start with the slope:
If two lines are perpendicular, their slopes are the negative reciprocal of each other.
The given line is: {{{highlight(y = 2x-4)}}}.  Since this is in the slope-intercept form: {{{y = mx+b}}} you can see that the slope {{{m = 2}}}.
The negative reciprocal of 2 is {{{-1/2}}}. 
So you can start with:
{{{y = (-1/2)x+b}}} but now you need to find the value of b, the y-intercept.
So we substitute the x- and y-coordinate values of the given point (4, 7) into the equation above and solve for b.
{{{7 = (-1/2)(4)+b}}} Simplify this:
{{{7 = -2+b}}} Add 2 to both sides.
{{{9 = b}}} Now that we have the value of b, we can write the final equation.
{{{highlight_green(y = (-1/2)x+9)}}}
And just to show you what these look like when graphed:
{{{graph(400,400,-5,20,-5,20,2x-4,(-1/2)x+9)}}}