Answer
$y = \dfrac{1}{2}x$
Work Step by Step
If two lines are parallel to one another, then they should have the same slope.
First, let us find the slope of the line given.
This line is written in standard form, so we want to rewrite this line in slope-intercept form, which is given by the following formula:
$y = mx + b$, where $m$ is the slope of the line and $b$ is the $y$-intercept.
We can rewrite our equation by isolating our $y$ term.
First, we subtract $x$ from each side of the equation:
$-2y = -x - 5$
Divide both sides of the equation by $-2$ to isolate $y$:
$y = \dfrac{1}{2}x + \dfrac{2}{5}$
So the slope of this line is the coefficient of $x$; in this case, the slope of this line is $\dfrac{1}{2}$. Therefore, the slope of the line whose equation we want to find is also $\frac{1}{2}$.
Let us plug this slope and the point we are given into the point-slope form of the equation, which is given by the formula:
$y - y_1 = m(x - x_1)$, where $m$ is the slope of the line and $(x_1, y_1)$ is a point on that line.
Let us use the point $(0, 0)$ to plug into the formula:
$y - 0 = \dfrac{1}{2}(x - 0)$
Simplify the equation:
$y = \dfrac{1}{2}x$
This equation is already in slope-intercept form, so we do not need to rewrite it any further.
