Answer
$y=-2x+4$
Work Step by Step
The slope of the line can be found as the product of the slopes of two perpendicular lines is $-1$.
Hence, the product of the slope of the line $x-2y=-5$ and the one we are trying to find is equal to $-1$.
The given line can be rewritten as: $y=\frac{1}{2}x+2.5$, in this form the coefficient of $x$ gives the slope.
Thus,
$m_1=\frac{1}{2}=0.5$
This means that the slope ($m_2$) of the line we are after can be found by having:
$0.5\times m_2=-1$
$m_2=-2$, this is the slope of the line we are trying to find.
If we have the slope and a point on the graph $(0,4)$ we can use the point-slope formula to calculate the equation of the line:
$y-y_1=m(x-x_1)$
$y-4=-2(x-0)$
$y-4=-2x$
$y=-2x+4$
