SOLUTION: I have a homework and I don't know how to resolve can you helpme please (8,2).m= - 3/4 (4,-5),m= - 1/2 write an equation of a line that passes through the y

Algebra ->  Linear-equations -> SOLUTION: I have a homework and I don't know how to resolve can you helpme please (8,2).m= - 3/4 (4,-5),m= - 1/2 write an equation of a line that passes through the y      Log On


   

Question 115225: I have a homework and I don't know how to resolve can you helpme please

(8,2).m= - 3/4
(4,-5),m= - 1/2
write an equation of a line that passes through the y-intercept -3 with slope 2.


Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
#1



If you want to find the equation of line with a given a slope of -3%2F4 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=%28-3%2F4%29%28x-8%29 Plug in m=-3%2F4, x%5B1%5D=8, and y%5B1%5D=2 (these values are given)


y-2=%28-3%2F4%29x%2B%28-3%2F4%29%28-8%29 Distribute -3%2F4

y-2=%28-3%2F4%29x%2B6 Multiply -3%2F4 and -8 to get 6

y=%28-3%2F4%29x%2B6%2B2 Add 2 to both sides to isolate y

y=%28-3%2F4%29x%2B8 Combine like terms 6 and 2 to get 8
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Answer:


So the equation of the line with a slope of -3%2F4 which goes through the point (8,2) is:

y=%28-3%2F4%29x%2B8 which is now in y=mx%2Bb form where the slope is m=-3%2F4 and the y-intercept is b=8

Notice if we graph the equation y=%28-3%2F4%29x%2B8 and plot the point (8,2), we get (note: if you need help with graphing, check out this solver)

Graph of y=%28-3%2F4%29x%2B8 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 -3%2F4 and goes through the point (8,2), this verifies our answer.



#2



If you want to find the equation of line with a given a slope of -1%2F2 which goes through the point (4,-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-4%29 Plug in m=-1%2F2, x%5B1%5D=4, and y%5B1%5D=-5 (these values are given)


y%2B5=%28-1%2F2%29%28x-4%29 Rewrite y--5 as y%2B5


y%2B5=%28-1%2F2%29x%2B%28-1%2F2%29%28-4%29 Distribute -1%2F2

y%2B5=%28-1%2F2%29x%2B2 Multiply -1%2F2 and -4 to get 2

y=%28-1%2F2%29x%2B2-5 Subtract 5 from both sides to isolate y

y=%28-1%2F2%29x-3 Combine like terms 2 and -5 to get -3
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Answer:


So the equation of the line with a slope of -1%2F2 which goes through the point (4,-5) is:

y=%28-1%2F2%29x-3 which is now in y=mx%2Bb form where the slope is m=-1%2F2 and the y-intercept is b=-3

Notice if we graph the equation y=%28-1%2F2%29x-3 and plot the point (4,-5), we get (note: if you need help with graphing, check out this solver)

Graph of y=%28-1%2F2%29x-3 through the point (4,-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 (4,-5), this verifies our answer.




#3

If we know that the y-intercept is -3, then the line goes through (0,-3)




If you want to find the equation of line with a given a slope of 2 which goes through the point (0,-3), 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--3=%282%29%28x-0%29 Plug in m=2, x%5B1%5D=0, and y%5B1%5D=-3 (these values are given)


y%2B3=%282%29%28x-0%29 Rewrite y--3 as y%2B3


y%2B3=2x%2B%282%29%28-0%29 Distribute 2

y%2B3=2x%2B0 Multiply 2 and -0 to get 0

y=2x%2B0-3 Subtract 3 from both sides to isolate y

y=2x-3 Combine like terms 0 and -3 to get -3
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Answer:


So the equation of the line with a slope of 2 which goes through the point (0,-3) is:

y=2x-3 which is now in y=mx%2Bb form where the slope is m=2 and the y-intercept is b=-3

Notice if we graph the equation y=2x-3 and plot the point (0,-3), we get (note: if you need help with graphing, check out this solver)

Graph of y=2x-3 through the point (0,-3)
and we can see that the point lies on the line. Since we know the equation has a slope of 2 and goes through the point (0,-3), this verifies our answer.