SOLUTION: What is the equation of a line going through points (0,5) (6,2)? Please and thank you.

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Question 77764: What is the equation of a line going through points (0,5) (6,2)? Please and thank you.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To find the equation, we first need to find the slope of the line going through (0,5) and (6,2):

Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (0,5) and (6,2)


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 (0,5) and (x%5B2%5D,y%5B2%5D) is the second point (6,2))


m=%282-5%29%2F%286-0%29 Plug in y%5B2%5D=2,y%5B1%5D=5,x%5B2%5D=6,x%5B1%5D=0 (these are the coordinates of given points)


m=+-3%2F6 Subtract the terms in the numerator 2-5 to get -3. Subtract the terms in the denominator 6-0 to get 6




m=-1%2F2 Reduce



So the slope is

m=-1%2F2





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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 (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-5=%28-1%2F2%29%28x-0%29 Plug in m=-1%2F2, x%5B1%5D=0, and y%5B1%5D=5 (these values are given)



y-5=%28-1%2F2%29x%2B%28-1%2F2%29%280%29 Distribute -1%2F2


y-5=%28-1%2F2%29x%2B0 Multiply -1%2F2 and 0 to get 0%2F2. Now reduce 0%2F2 to get 0

y=%28-1%2F2%29x%2B0%2B5 Add 5 to both sides to isolate y


y=%28-1%2F2%29x%2B5 Combine like terms 0 and 5 to get 5

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Answer:



So the equation of the line which goes through the points (0,5) and (6,2) is:y=%28-1%2F2%29x%2B5


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-1%2F2 and the y-intercept is b=5


Notice if we graph the equation y=%28-1%2F2%29x%2B5 and plot the points (0,5) and (6,2), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%28-1%2F2%29x%2B5 through the points (0,5) and (6,2)


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





So our equation is y=%28-1%2F2%29x%2B5