SOLUTION: i need step by step help please Write an equation of the line that passes through the given point P and has the given slope m 19. P(-8,-2),m-2/3 <its a fraction please h

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Question 105510This question is from textbook GEOMETRY
: i need step by step help please
Write an equation of the line that passes through the given point P and has the given slope m
19. P(-8,-2),m-2/3 please help This question is from textbook GEOMETRY

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 -2%2F3 which goes through the point (-8,-2), 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--2=%28-2%2F3%29%28x--8%29 Plug in m=-2%2F3, x%5B1%5D=-8, and y%5B1%5D=-2 (these values are given)


y%2B2=%28-2%2F3%29%28x--8%29 Rewrite y--2 as y%2B2


y%2B2=%28-2%2F3%29%28x%2B8%29 Rewrite x--8 as x%2B8


y%2B2=%28-2%2F3%29x%2B%28-2%2F3%29%288%29 Distribute -2%2F3

y%2B2=%28-2%2F3%29x-16%2F3 Multiply -2%2F3 and 8 to get -16%2F3

y=%28-2%2F3%29x-16%2F3-2 Subtract 2 from both sides to isolate y

y=%28-2%2F3%29x-22%2F3 Combine like terms -16%2F3 and -2 to get -22%2F3 (note: if you need help with combining fractions, check out this solver)


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Answer:


So the equation of the line with a slope of -2%2F3 which goes through the point (-8,-2) is:

y=%28-2%2F3%29x-22%2F3 which is now in y=mx%2Bb form where the slope is m=-2%2F3 and the y-intercept is b=-22%2F3

Notice if we graph the equation y=%28-2%2F3%29x-22%2F3 and plot the point (-8,-2), we get (note: if you need help with graphing, check out this solver)

Graph of y=%28-2%2F3%29x-22%2F3 through the point (-8,-2)
and we can see that the point lies on the line. Since we know the equation has a slope of -2%2F3 and goes through the point (-8,-2), this verifies our answer.