Answer
$\color{blue}{y=\frac{1}{2}x}$
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) Parallel lines have the same (equal) slopes.
(3) Perpendicular lines have slopes whose product is $-1$ (negative reciprocals of each other).
Write the given line in slope-intercept form to obtain:
$x-2y=-5
\\x+5=2y
\\\frac{x+5}{2} = \frac{2y}{2}
\\\frac{x}{2} + \frac{5}{2}=y
\\y=\frac{1}{2}x+\frac{5}{2}$
This line has a slope of $\frac{1}{2}$.
Since the line we are looking for is parallel to the line above, then its slope is also
$\\$ $\frac{1}{2}$.
Thus, the tentative equation of the line is:
$y=\frac{1}{2}x+b$
The line contains the point $(0, 0)$.
This means that the y-intercept of the line is $0$.
Therefore, the equation of the line is:
$y=\frac{1}{2}x+0
\\\color{blue}{y=\frac{1}{2}x}$
