SOLUTION: find the equation of the line which passes through the point (3,-7) and is parallel to the line 5x+y=13

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Question 343755: find the equation of the line which passes through the point (3,-7) and is parallel to the line 5x+y=13
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

Start with the given equation.


Subtract from both sides.


Rearrange the terms.


We can see that the equation has a slope and a y-intercept .


Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is .
Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope and the coordinates of the given point .


Start with the point slope formula


Plug in , , and


Rewrite as


Distribute


Multiply


Subtract 7 from both sides.


Combine like terms.


So the equation of the line parallel to that goes through the point is .


Here's a graph to visually verify our answer:
Graph of the original equation (red) and the parallel line (green) through the point .


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider making a donation at my tutoring website. Thank you.

Jim

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