SOLUTION: 5. Write the equation of the line containing the points (-4, 1) and (5, 2).

Algebra ->  Equations -> SOLUTION: 5. Write the equation of the line containing the points (-4, 1) and (5, 2).      Log On


   

Question 251376: 5. Write the equation of the line containing the points (-4, 1) and (5, 2).
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 (-4,1) and (5,2)


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


m=%282-1%29%2F%285--4%29 Plug in y%5B2%5D=2,y%5B1%5D=1,x%5B2%5D=5,x%5B1%5D=-4 (these are the coordinates of given points)


m=+1%2F9 Subtract the terms in the numerator 2-1 to get 1. Subtract the terms in the denominator 5--4 to get 9



So the slope is

m=1%2F9





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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-1=%281%2F9%29%28x--4%29 Plug in m=1%2F9, x%5B1%5D=-4, and y%5B1%5D=1 (these values are given)



y-1=%281%2F9%29%28x%2B4%29 Rewrite x--4 as x%2B4



y-1=%281%2F9%29x%2B%281%2F9%29%284%29 Distribute 1%2F9


y-1=%281%2F9%29x%2B4%2F9 Multiply 1%2F9 and 4 to get 4%2F9

y=%281%2F9%29x%2B4%2F9%2B1 Add 1 to both sides to isolate y


y=%281%2F9%29x%2B13%2F9 Combine like terms 4%2F9 and 1 to get 13%2F9 (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 (-4,1) and (5,2) is:y=%281%2F9%29x%2B13%2F9


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=1%2F9 and the y-intercept is b=13%2F9


Notice if we graph the equation y=%281%2F9%29x%2B13%2F9 and plot the points (-4,1) and (5,2), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%281%2F9%29x%2B13%2F9 through the points (-4,1) and (5,2)


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