SOLUTION: Write the equation of the line passing through (–3, –5) and (3, 0).

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Question 114788: Write the equation of the line passing through (–3, –5) and (3, 0).
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 (-3,-5) and (3,0)


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 (-3,-5) and (x%5B2%5D,y%5B2%5D) is the second point (3,0))


m=%280--5%29%2F%283--3%29 Plug in y%5B2%5D=0,y%5B1%5D=-5,x%5B2%5D=3,x%5B1%5D=-3 (these are the coordinates of given points)


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



So the slope is

m=5%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--5=%285%2F6%29%28x--3%29 Plug in m=5%2F6, x%5B1%5D=-3, and y%5B1%5D=-5 (these values are given)



y%2B5=%285%2F6%29%28x--3%29 Rewrite y--5 as y%2B5



y%2B5=%285%2F6%29%28x%2B3%29 Rewrite x--3 as x%2B3



y%2B5=%285%2F6%29x%2B%285%2F6%29%283%29 Distribute 5%2F6


y%2B5=%285%2F6%29x%2B5%2F2 Multiply 5%2F6 and 3 to get 15%2F6. Now reduce 15%2F6 to get 5%2F2

y=%285%2F6%29x%2B5%2F2-5 Subtract 5 from both sides to isolate y


y=%285%2F6%29x-5%2F2 Combine like terms 5%2F2 and -5 to get -5%2F2 (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 (-3,-5) and (3,0) is:y=%285%2F6%29x-5%2F2


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=5%2F6 and the y-intercept is b=-5%2F2


Notice if we graph the equation y=%285%2F6%29x-5%2F2 and plot the points (-3,-5) and (3,0), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%285%2F6%29x-5%2F2 through the points (-3,-5) and (3,0)


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