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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
Remember that y=mx%2Bb is the slope-intercept form of an equation where
'm' is the slope.


Looking at y=5x-6, we see that m=5, 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 y=5x-6, which has a slope of 5)


So we now know that m=5 for this unknown line.


Go back to y=mx%2Bb and plug it in to get y=5x%2Bb


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

1=5%281%29%2Bb


and solve for b to get:


1=5%281%29%2Bb
1=5%2Bb
1-5=b
-4=b
b=-4

So b=-4 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 m=5 and the y-intercept is (0,-4) making b=-4


So plug all of this new info into y=mx%2Bb to get y=5x-4


So the equation of the parallel line to y=5x-6 that goes through (1,1) is y=5x-4


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Answer

So the solution is y=5x-4



Here's a graph to visually verify our answer




Notice how the green line (the previously unknown equation y=5x-4) is parallel to the given red line (the given equation y=5x-6) and the green line goes through (1,1). So we've shown that our answer is correct.