SOLUTION: -4,7 and 2,-1

Algebra ->  Linear-equations -> SOLUTION: -4,7 and 2,-1      Log On


   

Question 1187947: -4,7 and 2,-1
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

assuming that
given points: (-4,7) and (2,-1)
find equation of the line
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (-4,7) and (2,-1)


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 (-4,7) and (x%5B2%5D,y%5B2%5D) is the second point (2,-1))


m=%28-1-7%29%2F%282--4%29 Plug in y%5B2%5D=-1,y%5B1%5D=7,x%5B2%5D=2,x%5B1%5D=-4 (these are the coordinates of given points)


m=+-8%2F6 Subtract the terms in the numerator -1-7 to get -8. Subtract the terms in the denominator 2--4 to get 6




m=-4%2F3 Reduce



So the slope is

m=-4%2F3





------------------------------------------------


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-7=%28-4%2F3%29%28x--4%29 Plug in m=-4%2F3, x%5B1%5D=-4, and y%5B1%5D=7 (these values are given)



y-7=%28-4%2F3%29%28x%2B4%29 Rewrite x--4 as x%2B4



y-7=%28-4%2F3%29x%2B%28-4%2F3%29%284%29 Distribute -4%2F3


y-7=%28-4%2F3%29x-16%2F3 Multiply -4%2F3 and 4 to get -16%2F3

y=%28-4%2F3%29x-16%2F3%2B7 Add 7 to both sides to isolate y


y=%28-4%2F3%29x%2B5%2F3 Combine like terms -16%2F3 and 7 to get 5%2F3 (note: if you need help with combining fractions, check out this solver)



------------------------------------------------------------------------------------------------------------

Answer:



So the equation of the line which goes through the points (-4,7) and (2,-1) is:y=%28-4%2F3%29x%2B5%2F3


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-4%2F3 and the y-intercept is b=5%2F3


Notice if we graph the equation y=%28-4%2F3%29x%2B5%2F3 and plot the points (-4,7) and (2,-1), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%28-4%2F3%29x%2B5%2F3 through the points (-4,7) and (2,-1)


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