SOLUTION: ok I suck at math and I need help with some homework. The main topic is finding the equation of a line using two points or a point and slope. I can give two examples of these quest

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Question 87742: ok I suck at math and I need help with some homework. The main topic is finding the equation of a line using two points or a point and slope. I can give two examples of these questions. one is this way:
(1,-2), m=2
and the other way is...
(-1,4)(2,-1)
please heeelp!


Found 2 solutions by sax101, jim_thompson5910:
Answer by sax101(1) About Me  (Show Source):
You can put this solution on YOUR website!
the equation to find slope is y2-y1 over x2-x1. since your points are (-1,4) and (2,-1) you plug in the numbers. So it should look like -1-4 over 2+1. you then solve it across and it equals -5/3.
y2 - y1
-------- = slope
x2 - x1

-1-4
-----
2+1
answer: -5/3

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 (1,-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 (x%5B1%5D,y%5B1%5D) is the given point

So lets use the Point-Slope Formula to find the equation of the line

y--2=%282%29%28x-1%29 Plug in m=2, x%5B1%5D=1, and y%5B1%5D=-2 (these values are given)

y--2=%282%29x-%282%29%281%29%29 Distribute 2

y--2=%282%29x%2B%28-2%29%281%29%29 Multiply the negatives

y%2B2=%282%29x%2B-2 Multiply -2 and 1 to get -2

y=%282%29x%2B-2%2B-2Subtract -2 from both sides


y=%282%29x%2B-4 Combine like terms
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Answer:


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

y=%282%29x%2B-4 which is now in y=mx%2Bb form where the slope is m=2 (so this shows our equation has a slope of 2) and the y-intercept is b=-4

Notice if we graph the equation y=%282%29x%2B-4 (note: if you need help with graphing, check out this solver) and plot the point (1,-2), we get

Graph of y=%282%29x%2B-4 through the point (1,-2)
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 (1,-2), this verifies our answer.
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#2
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (-1,4) and (2,-1)


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: (x%5B1%5D,y%5B1%5D) is the first point (-1,4) and (x%5B2%5D,y%5B2%5D) is the second point (2,-1))


m=%28-1-4%29%2F%282--1%29 Plug in y%5B2%5D=-1,y%5B1%5D=4,x%5B2%5D=2,x%5B1%5D=-1 (these are the coordinates of given points)


m=+-5%2F3 Subtract the terms in the numerator -1-4 to get -5. Subtract the terms in the denominator 2--1 to get 3



So the slope is

m=-5%2F3





------------------------------------------------


Now let's use the point-slope formula to find the equation of the line:




------Point-Slope Formula------
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and (x%5B1%5D,y%5B1%5D) is one of the given points


So lets use the Point-Slope Formula to find the equation of the line


y-4=%28-5%2F3%29%28x--1%29 Plug in m=-5%2F3, x%5B1%5D=-1, and y%5B1%5D=4 (these values are given)



y-4=%28-5%2F3%29%28x%2B1%29 Rewrite x--1 as x%2B1



y-4=%28-5%2F3%29x%2B%28-5%2F3%29%281%29 Distribute -5%2F3


y-4=%28-5%2F3%29x-5%2F3 Multiply -5%2F3 and 1 to get -5%2F3

y=%28-5%2F3%29x-5%2F3%2B4 Add 4 to both sides to isolate y


y=%28-5%2F3%29x%2B7%2F3 Combine like terms -5%2F3 and 4 to get 7%2F3 (note: if you need help with combining fractions, check out this solver)



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Answer:



So the equation of the line which goes through the points (-1,4) and (2,-1) is:y=%28-5%2F3%29x%2B7%2F3


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-5%2F3 and the y-intercept is b=7%2F3


Notice if we graph the equation y=%28-5%2F3%29x%2B7%2F3 and plot the points (-1,4) and (2,-1), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%28-5%2F3%29x%2B7%2F3 through the points (-1,4) and (2,-1)


Notice how the two points lie on the line. This graphically verifies our answer.