SOLUTION: find the slope intercept form of a line that passes through A(8,3) and B(-7,-5)

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Question 101416: find the slope intercept form of a line that passes through A(8,3) and B(-7,-5)
Answer by edjones(8007) 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 (8,3) and (-7,-5)


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 (8,3) and (x%5B2%5D,y%5B2%5D) is the second point (-7,-5))


m=%28-5-3%29%2F%28-7-8%29 Plug in y%5B2%5D=-5,y%5B1%5D=3,x%5B2%5D=-7,x%5B1%5D=8 (these are the coordinates of given points)


m=+-8%2F-15 Subtract the terms in the numerator -5-3 to get -8. Subtract the terms in the denominator -7-8 to get -15




m=8%2F15 Reduce



So the slope is

m=8%2F15





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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-3=%288%2F15%29%28x-8%29 Plug in m=8%2F15, x%5B1%5D=8, and y%5B1%5D=3 (these values are given)



y-3=%288%2F15%29x%2B%288%2F15%29%28-8%29 Distribute 8%2F15


y-3=%288%2F15%29x-64%2F15 Multiply 8%2F15 and -8 to get -64%2F15

y=%288%2F15%29x-64%2F15%2B3 Add 3 to both sides to isolate y


y=%288%2F15%29x-19%2F15 Combine like terms -64%2F15 and 3 to get -19%2F15 (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 (8,3) and (-7,-5) is:y=%288%2F15%29x-19%2F15


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=8%2F15 and the y-intercept is b=-19%2F15


Notice if we graph the equation y=%288%2F15%29x-19%2F15 and plot the points (8,3) and (-7,-5), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%288%2F15%29x-19%2F15 through the points (8,3) and (-7,-5)


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