SOLUTION: will you please explain to me how to do this using an equation. i am so lost. It says, find the slope and equation of the line through the points (-2,5) and (3,-1) If you could

Algebra ->  Linear-equations -> SOLUTION: will you please explain to me how to do this using an equation. i am so lost. It says, find the slope and equation of the line through the points (-2,5) and (3,-1) If you could       Log On


   

Question 93772: will you please explain to me how to do this using an equation. i am so lost.
It says, find the slope and equation of the line through the points (-2,5) and (3,-1)
If you could help me, that would be wonderful. thank you and God bless.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First lets find the slope through the points (-2,5) and (3,-1)

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula

m=%28-1-5%29%2F%283--2%29 Plug in y%5B2%5D=-1,y%5B1%5D=5,x%5B2%5D=3,x%5B1%5D=-2 (these are the coordinates of given points)

m=+-6%2F5 Subtract the terms in the numerator -1-5 to get -6. Subtract the terms in the denominator 3--2 to get 5

So the slope is
m=-6%2F5

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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 is one of the given points

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

y-5=%28-6%2F5%29%28x--2%29 Plug in m=-6%2F5, x%5B1%5D=-2, and y%5B1%5D=5 (these values are given)


y-5=%28-6%2F5%29%28x%2B2%29 Rewrite x--2 as x%2B2


y-5=%28-6%2F5%29x%2B%28-6%2F5%29%282%29 Distribute -6%2F5

y-5=%28-6%2F5%29x-12%2F5 Multiply -6%2F5 and 2 to get -12%2F5

y=%28-6%2F5%29x-12%2F5%2B5 Add 5 to both sides to isolate y

y=%28-6%2F5%29x%2B13%2F5 Combine like terms -12%2F5 and 5 to get 13%2F5 (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 (-2,5) and (3,-1) is:y=%28-6%2F5%29x%2B13%2F5

The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-6%2F5 and the y-intercept is b=13%2F5

Notice if we graph the equation y=%28-6%2F5%29x%2B13%2F5 and plot the points (-2,5) and (3,-1), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=%28-6%2F5%29x%2B13%2F5 through the points (-2,5) and (3,-1)