SOLUTION: directions: write an equation in point-slpoe form for the line through the given point with the given slope. these are the three problems i need help with: #1 (-2,7);m=2 #2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: directions: write an equation in point-slpoe form for the line through the given point with the given slope. these are the three problems i need help with: #1 (-2,7);m=2 #2       Log On


   

Question 113991: directions: write an equation in point-slpoe form for the line through the given point with the given slope.
these are the three problems i need help with:
#1 (-2,7);m=2
#2 (-5,-9);m=-3.5
#3 (4,0):m=7
p.s. do you mind showing me step by step because i get really confused
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 2 which goes through the point (-2,7), 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-7=%282%29%28x--2%29 Plug in m=2, x%5B1%5D=-2, and y%5B1%5D=7 (these values are given)


y-7=%282%29%28x%2B2%29 Rewrite x--2 as x%2B2


y-7=2x%2B%282%29%282%29 Distribute 2

y-7=2x%2B4 Multiply 2 and 2 to get 4

y=2x%2B4%2B7 Add 7 to both sides to isolate y

y=2x%2B11 Combine like terms 4 and 7 to get 11
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Answer:


So the equation of the line with a slope of 2 which goes through the point (-2,7) is:

y=2x%2B11 which is now in y=mx%2Bb form where the slope is m=2 and the y-intercept is b=11

Notice if we graph the equation y=2x%2B11 and plot the point (-2,7), we get (note: if you need help with graphing, check out this solver)

Graph of y=2x%2B11 through the point (-2,7)
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 (-2,7), this verifies our answer.



#2

Note: I'm going to write the slope -3.5 as -7%2F2




If you want to find the equation of line with a given a slope of -7%2F2 which goes through the point (-5,-9), 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--9=%28-7%2F2%29%28x--5%29 Plug in m=-7%2F2, x%5B1%5D=-5, and y%5B1%5D=-9 (these values are given)


y%2B9=%28-7%2F2%29%28x--5%29 Rewrite y--9 as y%2B9


y%2B9=%28-7%2F2%29%28x%2B5%29 Rewrite x--5 as x%2B5


y%2B9=%28-7%2F2%29x%2B%28-7%2F2%29%285%29 Distribute -7%2F2

y%2B9=%28-7%2F2%29x-35%2F2 Multiply -7%2F2 and 5 to get -35%2F2

y=%28-7%2F2%29x-35%2F2-9 Subtract 9 from both sides to isolate y

y=%28-7%2F2%29x-53%2F2 Combine like terms -35%2F2 and -9 to get -53%2F2 (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 -7%2F2 which goes through the point (-5,-9) is:

y=%28-7%2F2%29x-53%2F2 which is now in y=mx%2Bb form where the slope is m=-7%2F2 and the y-intercept is b=-53%2F2

Notice if we graph the equation y=%28-7%2F2%29x-53%2F2 and plot the point (-5,-9), we get (note: if you need help with graphing, check out this solver)

Graph of y=%28-7%2F2%29x-53%2F2 through the point (-5,-9)
and we can see that the point lies on the line. Since we know the equation has a slope of -7%2F2 and goes through the point (-5,-9), this verifies our answer.



#3



If you want to find the equation of line with a given a slope of 7 which goes through the point (4,0), 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-0=%287%29%28x-4%29 Plug in m=7, x%5B1%5D=4, and y%5B1%5D=0 (these values are given)


y-0=7x%2B%287%29%28-4%29 Distribute 7

y-0=7x-28 Multiply 7 and -4 to get -28

y=7x-28%2B0 Add 0 to both sides to isolate y

y=7x-28 Combine like terms -28 and 0 to get -28
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Answer:


So the equation of the line with a slope of 7 which goes through the point (4,0) is:

y=7x-28 which is now in y=mx%2Bb form where the slope is m=7 and the y-intercept is b=-28

Notice if we graph the equation y=7x-28 and plot the point (4,0), we get (note: if you need help with graphing, check out this solver)

Graph of y=7x-28 through the point (4,0)
and we can see that the point lies on the line. Since we know the equation has a slope of 7 and goes through the point (4,0), this verifies our answer.