Hi, there--

The Problem:
Find the equation of the line in standard form that is parallel to y=4x-2 and goes through 
(0,0).

Solution:
Your equation is in slope-intersept form, y = mx+b.
In this form, we can see that the slope of the line is 4 and the y-intercept is -2.

We want a parallel line. Parallel lines have the same slope, so the new slope is also 4.
Since the parallel goes through the origin, the y-intercept is 0. 

We can write the equation in slope-intercept form. The slope m=4 and the y-intercept b=0.




Your problem asks for the equation in standard form. Standard form looks like ax+by=c 
where a, b, and c are constants. Let's transform our equation to standard form.


Subtract 4x from both sides of the equation.


By convention, we usually make the leading coefficient positive. Multiply every term by -1.


That's it! If this explanation is unclear, or you still have questions, you may email me.

Mrs. Figgy
math.in.the.vortex@gmail.com