SOLUTION: I need a step-by step example of writing the equation of the line which passes through (5,-38) and (-1,3) write the answer in slope-intercept form. Please. :)

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Question 834734: I need a step-by step example of writing the equation of the line which passes through (5,-38) and (-1,3) write the answer in slope-intercept form. Please. :)
Answer by jim_thompson5910(35256) 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 (5,-38) and (-1,3)


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 (5,-38) and (x%5B2%5D,y%5B2%5D) is the second point (-1,3))


m=%283--38%29%2F%28-1-5%29 Plug in y%5B2%5D=3,y%5B1%5D=-38,x%5B2%5D=-1,x%5B1%5D=5 (these are the coordinates of given points)


m=+41%2F-6 Subtract the terms in the numerator 3--38 to get 41. Subtract the terms in the denominator -1-5 to get -6




m=-41%2F6 Reduce



So the slope is

m=-41%2F6





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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--38=%28-41%2F6%29%28x-5%29 Plug in m=-41%2F6, x%5B1%5D=5, and y%5B1%5D=-38 (these values are given)



y%2B38=%28-41%2F6%29%28x-5%29 Rewrite y--38 as y%2B38



y%2B38=%28-41%2F6%29x%2B%28-41%2F6%29%28-5%29 Distribute -41%2F6


y%2B38=%28-41%2F6%29x%2B205%2F6 Multiply -41%2F6 and -5 to get 205%2F6

y=%28-41%2F6%29x%2B205%2F6-38 Subtract 38 from both sides to isolate y


y=%28-41%2F6%29x-23%2F6 Combine like terms 205%2F6 and -38 to get -23%2F6 (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 (5,-38) and (-1,3) is:y=%28-41%2F6%29x-23%2F6


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-41%2F6 and the y-intercept is b=-23%2F6


Notice if we graph the equation y=%28-41%2F6%29x-23%2F6 and plot the points (5,-38) and (-1,3), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%28-41%2F6%29x-23%2F6 through the points (5,-38) and (-1,3)


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





Note: the graph for this solver is a bit off, so don't mind that. The rest of the solver is correct though.