SOLUTION: write an equation of the line which has the given slope, m, and which passes through the given point. m = -1/2; (8,-5)

Algebra ->  Linear-equations -> SOLUTION: write an equation of the line which has the given slope, m, and which passes through the given point. m = -1/2; (8,-5)      Log On


   

Question 93786: write an equation of the line which has the given slope, m, and which passes through the given point. m = -1/2; (8,-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 -1%2F2 which goes through the point (8,-5), 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--5=%28-1%2F2%29%28x-8%29 Plug in m=-1%2F2, x%5B1%5D=8, and y%5B1%5D=-5 (these values are given)


y%2B5=%28-1%2F2%29%28x-8%29 Rewrite y--5 as y%2B5


y%2B5=%28-1%2F2%29x%2B%28-1%2F2%29%28-8%29 Distribute -1%2F2

y%2B5=%28-1%2F2%29x%2B4 Multiply -1%2F2 and -8 to get 4

y=%28-1%2F2%29x%2B4-5 Subtract 5 from both sides to isolate y

y=%28-1%2F2%29x-1 Combine like terms 4 and -5 to get -1
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Answer:


So the equation of the line with a slope of -1%2F2 which goes through the point (8,-5) is:

y=%28-1%2F2%29x-1 which is now in y=mx%2Bb form where the slope is m=-1%2F2 and the y-intercept is b=-1

Notice if we graph the equation y=%28-1%2F2%29x-1 and plot the point (8,-5), we get (note: if you need help with graphing, check out this solver)

Graph of y=%28-1%2F2%29x-1 through the point (8,-5)
and we can see that the point lies on the line. Since we know the equation has a slope of -1%2F2 and goes through the point (8,-5), this verifies our answer.