SOLUTION: Use point-slope form to determine the equation of hte line passing through the two given points. Then write the equation in slope-intercept form. (4,3), (2,-9).

Algebra ->  Linear-equations -> SOLUTION: Use point-slope form to determine the equation of hte line passing through the two given points. Then write the equation in slope-intercept form. (4,3), (2,-9).      Log On


   

Question 111444: Use point-slope form to determine the equation of hte line passing through the two given points. Then write the equation in slope-intercept form.
(4,3), (2,-9).
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 (4,3) and (2,-9)


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 (4,3) and (x%5B2%5D,y%5B2%5D) is the second point (2,-9))


m=%28-9-3%29%2F%282-4%29 Plug in y%5B2%5D=-9,y%5B1%5D=3,x%5B2%5D=2,x%5B1%5D=4 (these are the coordinates of given points)


m=+-12%2F-2 Subtract the terms in the numerator -9-3 to get -12. Subtract the terms in the denominator 2-4 to get -2




m=6 Reduce



So the slope is

m=6





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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=%286%29%28x-4%29 Plug in m=6, x%5B1%5D=4, and y%5B1%5D=3 (these values are given)



y-3=6x%2B%286%29%28-4%29 Distribute 6


y-3=6x-24 Multiply 6 and -4 to get -24%2F1. Now reduce -24%2F1 to get -24

y=6x-24%2B3 Add 3 to both sides to isolate y


y=6x-21 Combine like terms -24 and 3 to get -21

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Answer:



So the equation of the line which goes through the points (4,3) and (2,-9) is:y=6x-21


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=6 and the y-intercept is b=-21


Notice if we graph the equation y=6x-21 and plot the points (4,3) and (2,-9), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=6x-21 through the points (4,3) and (2,-9)


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