SOLUTION: Write the equation of the line that passes through point (–5, 18) with a slope of –5.

Algebra ->  Coordinate-system -> SOLUTION: Write the equation of the line that passes through point (–5, 18) with a slope of –5.      Log On


   

Question 117204: Write the equation of the line that passes through point (–5, 18) with a slope of –5.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

If you want to find the equation of line with a given a slope of -5 which goes through the point (-5,18), you can simply use the point-slope formula to find the equation:


---Point-Slope Formula---
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and is the given point

So lets use the Point-Slope Formula to find the equation of the line

y-18=%28-5%29%28x--5%29 Plug in m=-5, x%5B1%5D=-5, and y%5B1%5D=18 (these values are given)


y-18=%28-5%29%28x%2B5%29 Rewrite x--5 as x%2B5


y-18=-5x%2B%28-5%29%285%29 Distribute -5

y-18=-5x-25 Multiply -5 and 5 to get -25

y=-5x-25%2B18 Add 18 to both sides to isolate y

y=-5x-7 Combine like terms -25 and 18 to get -7
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Answer:


So the equation of the line with a slope of -5 which goes through the point (-5,18) is:

y=-5x-7 which is now in y=mx%2Bb form where the slope is m=-5 and the y-intercept is b=-7

Notice if we graph the equation y=-5x-7 and plot the point (-5,18), we get (note: if you need help with graphing, check out this solver)

Graph of y=-5x-7 through the point (-5,18)
and we can see that the point lies on the line. Since we know the equation has a slope of -5 and goes through the point (-5,18), this verifies our answer.