SOLUTION: Hi, I have 6 problems that I just cant seem to get. I've been all around sites to see if any could help me with them but I couldnt find one until I came here. So my questions are:

Algebra ->  Linear-equations -> SOLUTION: Hi, I have 6 problems that I just cant seem to get. I've been all around sites to see if any could help me with them but I couldnt find one until I came here. So my questions are:      Log On


   

Question 115201: Hi, I have 6 problems that I just cant seem to get. I've been all around sites to see if any could help me with them but I couldnt find one until I came here.
So my questions are:
1. (-3,1), m=2
2. (-6,1), m=4
3. (10,4), m is undefined
4. (6,5), m=0
5. (4,0), m= -1
6. (9,-12), m=-1/2
My teacher just gave my class this homework today and didn't explain it at all. So I'm hoping you can.
Thanks So Much
Em
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
There are a lot of problems here. So I'll do a few to help you get started
#1


If you want to find the equation of line with a given a slope of 2 which goes through the point (-3,1), 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-1=%282%29%28x--3%29 Plug in m=2, x%5B1%5D=-3, and y%5B1%5D=1 (these values are given)


y-1=%282%29%28x%2B3%29 Rewrite x--3 as x%2B3


y-1=2x%2B%282%29%283%29 Distribute 2

y-1=2x%2B6 Multiply 2 and 3 to get 6

y=2x%2B6%2B1 Add 1 to both sides to isolate y

y=2x%2B7 Combine like terms 6 and 1 to get 7
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Answer:


So the equation of the line with a slope of 2 which goes through the point (-3,1) is:

y=2x%2B7 which is now in y=mx%2Bb form where the slope is m=2 and the y-intercept is b=7

Notice if we graph the equation y=2x%2B7 and plot the point (-3,1), we get (note: if you need help with graphing, check out this solver)

Graph of y=2x%2B7 through the point (-3,1)
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 (-3,1), 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 (-6,1), 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-1=%284%29%28x--6%29 Plug in m=4, x%5B1%5D=-6, and y%5B1%5D=1 (these values are given)


y-1=%284%29%28x%2B6%29 Rewrite x--6 as x%2B6


y-1=4x%2B%284%29%286%29 Distribute 4

y-1=4x%2B24 Multiply 4 and 6 to get 24

y=4x%2B24%2B1 Add 1 to both sides to isolate y

y=4x%2B25 Combine like terms 24 and 1 to get 25
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Answer:


So the equation of the line with a slope of 4 which goes through the point (-6,1) is:

y=4x%2B25 which is now in y=mx%2Bb form where the slope is m=4 and the y-intercept is b=25

Notice if we graph the equation y=4x%2B25 and plot the point (-6,1), we get (note: if you need help with graphing, check out this solver)

Graph of y=4x%2B25 through the point (-6,1)
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 (-6,1), this verifies our answer.



#3

If you want to find the equation of line with an undefined slope which goes through the point (10,4), simply draw a vertical line through x=10:

Graph of x=10

So this simply means that the equation of the line is x=10 (notice y is not in the equation. So this means this equation is not in slope-intercept form)