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) About Me  (Show Source):
You can put this solution on YOUR website!

5x%2By=13 Start with the given equation.


y=13-5x Subtract 5x from both sides.


y=-5x%2B13 Rearrange the terms.


We can see that the equation y=-5%2Ax%2B13 has a slope m=-5 and a y-intercept b=13.


Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is m=-5.
Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope m=-5 and the coordinates of the given point .


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y--7=-5%28x-3%29 Plug in m=-5, x%5B1%5D=3, and y%5B1%5D=-7


y%2B7=-5%28x-3%29 Rewrite y--7 as y%2B7


y%2B7=-5x%2B-5%28-3%29 Distribute


y%2B7=-5x%2B15 Multiply


y=-5x%2B15-7 Subtract 7 from both sides.


y=-5x%2B8 Combine like terms.


So the equation of the line parallel to 5x%2By=13 that goes through the point is y=-5x%2B8.


Here's a graph to visually verify our answer:
Graph of the original equation y=-5%2Ax%2B13 (red) and the parallel line y=-5x%2B8 (green) through the point .


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

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Jim