SOLUTION: What is the equation of the line, in general form, that passes through the point (1, 1) and has a y-intercept of 2

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Question 687578: What is the equation of the line, in general form, that passes through the point (1, 1) and has a y-intercept of 2
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

the equation of the line, in general form, that passes through the point
(1, 1) and has a y-intercept of 2 (which is a point
(0,2) ) will be:

Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (1,1) and (0,2)


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


m=%282-1%29%2F%280-1%29 Plug in y%5B2%5D=2,y%5B1%5D=1,x%5B2%5D=0,x%5B1%5D=1 (these are the coordinates of given points)


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




m=-1 Reduce



So the slope is

m=-1





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



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


y-1=-x%2B1 Multiply -1 and -1 to get 1%2F1. Now reduce 1%2F1 to get 1

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


y=-x%2B2 Combine like terms 1 and 1 to get 2

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Answer:



So the equation of the line which goes through the points (1,1) and (0,2) is:y=-x%2B2


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


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


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


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