SOLUTION: Question: Write an equation of the line that passes through each point with the given slope. (1,-4),m=-6

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Question 175491: Question: Write an equation of the line that passes through each point with the given slope. (1,-4),m=-6
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 -6 which goes through the point (1,-4), 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--4=%28-6%29%28x-1%29 Plug in m=-6, x%5B1%5D=1, and y%5B1%5D=-4 (these values are given)


y%2B4=%28-6%29%28x-1%29 Rewrite y--4 as y%2B4


y%2B4=-6x%2B%28-6%29%28-1%29 Distribute -6

y%2B4=-6x%2B6 Multiply -6 and -1 to get 6

y=-6x%2B6-4 Subtract 4 from both sides to isolate y

y=-6x%2B2 Combine like terms 6 and -4 to get 2
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Answer:


So the equation of the line with a slope of -6 which goes through the point (1,-4) is:

y=-6x%2B2 which is now in y=mx%2Bb form where the slope is m=-6 and the y-intercept is b=2

Notice if we graph the equation y=-6x%2B2 and plot the point (1,-4), we get (note: if you need help with graphing, check out this solver)

Graph of y=-6x%2B2 through the point (1,-4)
and we can see that the point lies on the line. Since we know the equation has a slope of -6 and goes through the point (1,-4), this verifies our answer.