SOLUTION: find the equation of the line that goes through the given point and has the given slope. write the answer in slope-intercept form. (-1,-5), -8

Algebra ->  Linear-equations -> SOLUTION: find the equation of the line that goes through the given point and has the given slope. write the answer in slope-intercept form. (-1,-5), -8      Log On


   

Question 219616: find the equation of the line that goes through the given point and has the given slope. write the answer in slope-intercept form.
(-1,-5), -8
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 -8 which goes through the point (-1,-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=%28-8%29%28x--1%29 Plug in m=-8, x%5B1%5D=-1, and y%5B1%5D=-5 (these values are given)


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


y%2B5=%28-8%29%28x%2B1%29 Rewrite x--1 as x%2B1


y%2B5=-8x%2B%28-8%29%281%29 Distribute -8


y%2B5=-8x-8 Multiply -8 and 1 to get -8


y=-8x-8-5 Subtract 5 from both sides to isolate y


y=-8x-13 Combine like terms -8 and -5 to get -13
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Answer:


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

y=-8x-13 which is now in y=mx%2Bb form where the slope is m=-8 and the y-intercept is b=-13

Notice if we graph the equation y=-8x-13 and plot the point (-1,-5), we get (note: if you need help with graphing, check out this solver)

Graph of y=-8x-13 through the point (-1,-5)
and we can see that the point lies on the line. Since we know the equation has a slope of -8 and goes through the point (-1,-5), this verifies our answer.