SOLUTION: Find an equation of the line that passes through the points (1, 4) and ( -7, -4)

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Question 954297: Find an equation of the line that passes through the points (1, 4) and ( -7, -4)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (1,4) and (-7,-4)


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 (-7,-4))


m=%28-4-4%29%2F%28-7-1%29 Plug in y%5B2%5D=-4,y%5B1%5D=4,x%5B2%5D=-7,x%5B1%5D=1 (these are the coordinates of given points)


m=+-8%2F-8 Subtract the terms in the numerator -4-4 to get -8. Subtract the terms in the denominator -7-1 to get -8




m=1 Reduce



So the slope is

m=1





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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-4=%281%29%28x-1%29 Plug in m=1, x%5B1%5D=1, and y%5B1%5D=4 (these values are given)



y-4=1x%2B%281%29%28-1%29 Distribute 1


y-4=1x-1 Multiply 1 and -1 to get -1%2F1. Now reduce -1%2F1 to get -1

y=1x-1%2B4 Add 4 to both sides to isolate y


y=1x%2B3 Combine like terms -1 and 4 to get 3

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Answer:



So the equation of the line which goes through the points (1,4) and (-7,-4) is:y=1x%2B3


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=1 and the y-intercept is b=3


Notice if we graph the equation y=1x%2B3 and plot the points (1,4) and (-7,-4), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=1x%2B3 through the points (1,4) and (-7,-4)


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