SOLUTION: How do I find the equation of the line passing through the point (1,1) and parallel to y=5x-6? I am having a very tough time figuring this problem, any help is greatly appreciat

Question 403352: How do I find the equation of the line passing through the point (1,1) and parallel to y=5x-6?
I am having a very tough time figuring this problem, any help is greatly appreciated! Thank you!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Remember that is the slope-intercept form of an equation where
'm' is the slope.

Looking at , we see that , which means that the slope is 5.

Also, remember that any two parallel lines have the same slope. So the slope of the unknown parallel line is 5 (since it's parallel to , which has a slope of 5)

So we now know that for this unknown line.

Go back to and plug it in to get

Now we're forcing this new unknown line to go through (1,1). So when x=1, y=1. Plug these values in to get

and solve for b to get:

So which is the last piece of the puzzle. So the y-intercept of this unknown line is (0,-4) because all y-intercepts are of the form (0, some number)

So in summary, we know that the unknown (soon not really unknown) line has a slope of 5, so and the y-intercept is (0,-4) making

So plug all of this new info into to get

So the equation of the parallel line to that goes through (1,1) is

------------------------------------------------------------------------
Answer

So the solution is

Here's a graph to visually verify our answer

Notice how the green line (the previously unknown equation ) is parallel to the given red line (the given equation ) and the green line goes through (1,1). So we've shown that our answer is correct.
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