Parallel lines have the same slope. Let's start by considering the given line.
y=7x-3
We see that the slope is 7. Therefore, all parallel lines to the given one will have a slope of 7. Let's write a partial equation of these lines in slope-intercept form.
y=7x+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=7x-3 through the origin.
y=7x+ 0 ⇔ y=7x
Alternative Solution
Another way of finding the y-intercept
If the lines are parallel, then they have the same slope. We can write a partial equation of our line.
y=7x+b
Since we are told the line passes through the origin, we know its y-intercept is b=0.
y=7x+0 ⇔ y=7x
