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Parallel lines have the same slope. Let's start by considering the given line.
$y=5x−2 $
We see that the slope is $5.$ Therefore, *all* parallel lines to the given one will have a slope of $5.$ Let's write a partial equation of these lines in slope-intercept form.
$y=5x+b $
Finally, we are told that the line whose equation we are asked to write passes through the origin. To find its $y-$intercept $b,$ we will substitute $0$ for $x$ and $y.$
Now that we know that $b=0,$ we can write the equation of the parallel line to $y=5x−2$ through the origin.
$y=5x+b⇔y=5x $
### Alternative Solution

Another way of finding the $y-$intercept

$y=5x+b$

$0=5⋅0+b$

Solve for $b$

$b=0$

If the lines are parallel, then they have the same slope. We can write a partial equation of our line. $y=5x+b $ Since we are told the line passes through the origin, we know its $y-$intercept is $b=0.$ $y=5x+0⇔y=5x $