SOLUTION: 19. Write the equation of the line that passes through point (–2, –18) with a slope of 8.

Algebra ->  Coordinate-system -> SOLUTION: 19. Write the equation of the line that passes through point (–2, –18) with a slope of 8.      Log On


   

Question 110380: 19. Write the equation of the line that passes through point (–2, –18) with a slope of 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 (-2,-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=%288%29%28x--2%29 Plug in m=8, x%5B1%5D=-2, and y%5B1%5D=-18 (these values are given)


y%2B18=%288%29%28x--2%29 Rewrite y--18 as y%2B18


y%2B18=%288%29%28x%2B2%29 Rewrite x--2 as x%2B2


y%2B18=8x%2B%288%29%282%29 Distribute 8

y%2B18=8x%2B16 Multiply 8 and 2 to get 16

y=8x%2B16-18 Subtract 18 from both sides to isolate y

y=8x-2 Combine like terms 16 and -18 to get -2
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Answer:


So the equation of the line with a slope of 8 which goes through the point (-2,-18) is:

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

Notice if we graph the equation y=8x-2 and plot the point (-2,-18), we get (note: if you need help with graphing, check out this solver)

Graph of y=8x-2 through the point (-2,-18)
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 (-2,-18), this verifies our answer.