SOLUTION: find the equation of the line P1(0,3) P2(-1,0)

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Question 1125239: find the equation of the line P1(0,3) P2(-1,0)
Answer by MathLover1(20850) 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 (0,3) and (-1,0)


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 (0,3) and (x%5B2%5D,y%5B2%5D) is the second point (-1,0))


m=%280-3%29%2F%28-1-0%29 Plug in y%5B2%5D=0,y%5B1%5D=3,x%5B2%5D=-1,x%5B1%5D=0 (these are the coordinates of given points)


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




m=3 Reduce



So the slope is

m=3





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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=%283%29%28x-0%29 Plug in m=3, x%5B1%5D=0, and y%5B1%5D=3 (these values are given)



y-3=3x%2B%283%29%280%29 Distribute 3


y-3=3x%2B0 Multiply 3 and 0 to get 0%2F1. Now reduce 0%2F1 to get 0

y=3x%2B0%2B3 Add 3 to both sides to isolate y


y=3x%2B3 Combine like terms 0 and 3 to get 3

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Answer:



So the equation of the line which goes through the points (0,3) and (-1,0) is:y=3x%2B3


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


Notice if we graph the equation y=3x%2B3 and plot the points (0,3) and (-1,0), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=3x%2B3 through the points (0,3) and (-1,0)


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