SOLUTION: If the slope is negative one-fourth (-1/4) and passes through the point (4,4), what's the equation in the form y=mx+b? If the slope is 4 and the y intercept is (0,12), what's th

Algebra ->  Linear-equations -> SOLUTION: If the slope is negative one-fourth (-1/4) and passes through the point (4,4), what's the equation in the form y=mx+b? If the slope is 4 and the y intercept is (0,12), what's th      Log On


   

Question 130249: If the slope is negative one-fourth (-1/4) and passes through the point (4,4), what's the equation in the form y=mx+b?
If the slope is 4 and the y intercept is (0,12), what's the equation in the form y=mx+b?
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 -1%2F4 which goes through the point (4,4), 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-4=%28-1%2F4%29%28x-4%29 Plug in m=-1%2F4, x%5B1%5D=4, and y%5B1%5D=4 (these values are given)


y-4=%28-1%2F4%29x%2B%28-1%2F4%29%28-4%29 Distribute -1%2F4

y-4=%28-1%2F4%29x%2B1 Multiply -1%2F4 and -4 to get 1

y=%28-1%2F4%29x%2B1%2B4 Add 4 to both sides to isolate y

y=%28-1%2F4%29x%2B5 Combine like terms 1 and 4 to get 5
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Answer:


So the equation of the line with a slope of -1%2F4 which goes through the point (4,4) is:

y=%28-1%2F4%29x%2B5 which is now in y=mx%2Bb form where the slope is m=-1%2F4 and the y-intercept is b=5

Notice if we graph the equation y=%28-1%2F4%29x%2B5 and plot the point (4,4), we get (note: if you need help with graphing, check out this solver)

Graph of y=%28-1%2F4%29x%2B5 through the point (4,4)
and we can see that the point lies on the line. Since we know the equation has a slope of -1%2F4 and goes through the point (4,4), this verifies our answer.




# 2


If you want to find the equation of line with a given a slope of 4 which goes through the point (0,12), 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-12=%284%29%28x-0%29 Plug in m=4, x%5B1%5D=0, and y%5B1%5D=12 (these values are given)


y-12=4x%2B%284%29%28-0%29 Distribute 4

y-12=4x%2B0 Multiply 4 and -0 to get 0

y=4x%2B0%2B12 Add 12 to both sides to isolate y

y=4x%2B12 Combine like terms 0 and 12 to get 12
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Answer:


So the equation of the line with a slope of 4 which goes through the point (0,12) is:

y=4x%2B12 which is now in y=mx%2Bb form where the slope is m=4 and the y-intercept is b=12

Notice if we graph the equation y=4x%2B12 and plot the point (0,12), we get (note: if you need help with graphing, check out this solver)

Graph of y=4x%2B12 through the point (0,12)
and we can see that the point lies on the line. Since we know the equation has a slope of 4 and goes through the point (0,12), this verifies our answer.