SOLUTION: Find an equation of a line through (1,1) and (-2,0)in standard form.

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Question 89841: Find an equation of a line through (1,1) and (-2,0)in standard form.
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 (1,1) and (-2,0)


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 (1,1) and (x%5B2%5D,y%5B2%5D) is the second point (-2,0))


m=%280-1%29%2F%28-2-1%29 Plug in y%5B2%5D=0,y%5B1%5D=1,x%5B2%5D=-2,x%5B1%5D=1 (these are the coordinates of given points)


m=+-1%2F-3 Subtract the terms in the numerator 0-1 to get -1. Subtract the terms in the denominator -2-1 to get -3




m=1%2F3 Reduce



So the slope is

m=1%2F3





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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%2F3%29%28x-1%29 Plug in m=1%2F3, x%5B1%5D=1, and y%5B1%5D=1 (these values are given)



y-1=%281%2F3%29x%2B%281%2F3%29%28-1%29 Distribute 1%2F3


y-1=%281%2F3%29x-1%2F3 Multiply 1%2F3 and -1 to get -1%2F3

y=%281%2F3%29x-1%2F3%2B1 Add 1 to both sides to isolate y


y=%281%2F3%29x%2B2%2F3 Combine like terms -1%2F3 and 1 to get 2%2F3 (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 (1,1) and (-2,0) is:y=%281%2F3%29x%2B2%2F3


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=1%2F3 and the y-intercept is b=2%2F3


Notice if we graph the equation y=%281%2F3%29x%2B2%2F3 and plot the points (1,1) and (-2,0), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%281%2F3%29x%2B2%2F3 through the points (1,1) and (-2,0)


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





Now lets convert to standard form

Solved by pluggable solver: Converting Linear Equations in Standard form to Slope-Intercept Form (and vice versa)
Convert from slope-intercept form (y = mx+b) to standard form (Ax+By = C)


y+=+%281%2F3%29x%2B2%2F3 Start with the given equation


3%2Ay+=+3%2A%28%281%2F3%29x%2B2%2F3%29 Multiply both sides by the LCD 3


3y+=+1x%2B2 Distribute and multiply


3y-1x+=+1x%2B2-1x Subtract 1x from both sides


-1x%2B3y+=+2 Simplify


-1%2A%28-1x%2B3y%29+=+-1%2A%282%29 Multiply both sides by -1 to make the A coefficient positive (note: this step may be optional; it will depend on your teacher and/or textbook)


1x-3y+=+-2 Distribute and simplify


The original equation y+=+%281%2F3%29x%2B2%2F3 (slope-intercept form) is equivalent to 1x-3y+=+-2 (standard form where A > 0)


The equation 1x-3y+=+-2 is in the form Ax%2BBy+=+C where A+=+1, B+=+-3 and C+=+-2