SOLUTION: How to convert a point into a point-slope, slope-intercept and standard form? Ex: (6,1), (4,1)

Algebra ->  Linear-equations -> SOLUTION: How to convert a point into a point-slope, slope-intercept and standard form? Ex: (6,1), (4,1)      Log On


   

Question 112351: How to convert a point into a point-slope, slope-intercept and standard form?
Ex: (6,1), (4,1)
Found 2 solutions by checkley71, jim_thompson5910:
Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
THE BEST WAY TO SEE THIS TYPE OF PROBLEM IS TO USE GRAPH PAPER & PLOT THE 2 POINTS & THEN DRAW THE LINE THROUGH THEM.
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FIRST YOU NEED TO FIND THE SLOPE
(Y2-Y1)/(X2-X1)
(1-1)/(4-6)
0/-2 OR A ZERO SLOPE WHICH IS A HORIZONTAL LINE THROUGH Y=1
Y=1 IS ALSO THE LINE EQUATION.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Do you want to find the equation through these two points? If you do, then to find the equation of the line, we need to find the slope through the two points


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: is the first point (6,1) and is the second point (4,1))

m=%281-1%29%2F%284-6%29 Plug in y%5B2%5D=1,y%5B1%5D=1,x%5B2%5D=4,x%5B1%5D=6 (these are the coordinates of given points)

m=+0%2F-2 Subtract the terms in the numerator 1-1 to get 0. Subtract the terms in the denominator 4-6 to get -2


m=0 Reduce

So the slope is
m=0

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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 is one of the given points

So lets use the Point-Slope Formula to find the equation of the line

y-1=%280%29%28x-6%29 Plug in m=0, x%5B1%5D=6, and y%5B1%5D=1 (these values are given)


y-1=0x%2B%280%29%28-6%29 Distribute 0

y-1=0x%2B0 Multiply 0 and -6 to get 0%2F0. Now reduce 0%2F0 to get 0

y=0x%2B0%2B1 Add 1 to both sides to isolate y

y=0x%2B1 Combine like terms 0 and 1 to get 1
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Answer:


So the equation of the line which goes through the points (6,1) and (4,1) is:y=0x%2B1

The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=0 and the y-intercept is b=1

Notice if we graph the equation y=0x%2B1 and plot the points (6,1) and (4,1), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=0x%2B1 through the points (6,1) and (4,1)

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