SOLUTION: Find the slope of the line that passes through (6,-2) and (-3,2) Find the equation of a line that passes through the points (-11,-4) and (9,8)

Algebra ->  Graphs -> SOLUTION: Find the slope of the line that passes through (6,-2) and (-3,2) Find the equation of a line that passes through the points (-11,-4) and (9,8)      Log On


   

Question 932097: Find the slope of the line that passes through (6,-2) and (-3,2)
Find the equation of a line that passes through the points (-11,-4) and (9,8)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Find the slope of the line that passes through (6,-2) and (-3,2):

Solved by pluggable solver: Finding the slope


Slope of the line through the points (6, -2) and (-3, 2)



m+=+%28y%5B2%5D+-+%28y%5B1%5D%29%29%2F%28x%5B2%5D+-+x%5B1%5D%29


m+=+%282+-+%28-2%29%29%2F%28-3+-+6%29


m+=+%282+%2B+2%29%2F%28-3+-+6%29


m+=+%284%29%2F%28-9%29


m+=+-4%2F9



Answer: Slope is m+=+-4%2F9



Find the equation of a line that passes through the points (-11,-4) and (9,8):
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (-11,-4) and (9,8)


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 (-11,-4) and (x%5B2%5D,y%5B2%5D) is the second point (9,8))


m=%288--4%29%2F%289--11%29 Plug in y%5B2%5D=8,y%5B1%5D=-4,x%5B2%5D=9,x%5B1%5D=-11 (these are the coordinates of given points)


m=+12%2F20 Subtract the terms in the numerator 8--4 to get 12. Subtract the terms in the denominator 9--11 to get 20




m=3%2F5 Reduce



So the slope is

m=3%2F5





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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=%283%2F5%29%28x--11%29 Plug in m=3%2F5, x%5B1%5D=-11, and y%5B1%5D=-4 (these values are given)



y%2B4=%283%2F5%29%28x--11%29 Rewrite y--4 as y%2B4



y%2B4=%283%2F5%29%28x%2B11%29 Rewrite x--11 as x%2B11



y%2B4=%283%2F5%29x%2B%283%2F5%29%2811%29 Distribute 3%2F5


y%2B4=%283%2F5%29x%2B33%2F5 Multiply 3%2F5 and 11 to get 33%2F5

y=%283%2F5%29x%2B33%2F5-4 Subtract 4 from both sides to isolate y


y=%283%2F5%29x%2B13%2F5 Combine like terms 33%2F5 and -4 to get 13%2F5 (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 (-11,-4) and (9,8) is:y=%283%2F5%29x%2B13%2F5


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=3%2F5 and the y-intercept is b=13%2F5


Notice if we graph the equation y=%283%2F5%29x%2B13%2F5 and plot the points (-11,-4) and (9,8), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%283%2F5%29x%2B13%2F5 through the points (-11,-4) and (9,8)


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





since you can't see the points, here is another graph: