Answer
$\color{blue}{y=-2x+4}$
Work Step by Step
RECALL:
(1) The slope-intercept form of a line's equation is:
$y=mx+b$
where $m$ = slope and $b$ = y-intercept
(2) Perpendicular lines have slopes whose product is $-1$ (negative reciprocals of each other).
Write the equation of the given line in slope-intercept method to obtain:
$x-2y=-5
\\x+5=2y
\\\frac{x+5}{2}=\frac{2y}{2}
\\\frac{x}{2} + \frac{5}{2} = y
\\y=\frac{1}{2}x+\frac{5}{2}$
The line we are looking for is perpendicular to the line above (whose slope is $\frac{1}{2}$).
This means that the line has a slope of $-2$ (since $\frac{1}{2}(-2)=-1$).
Thus, a tentative equation of the line we are looking for is:
$y=-2x+b$
To find the value of $b$, substitute the x and y values of the given point to obtain:
$y=-2x+b
\\4 = -2(0)+b
\\4=0+b
\\4 =b$
Thus, the equation of the line is:
$\color{blue}{y=-2x+4}$
