SOLUTION: What would the equation be for the line that passes throught the points (2,3) and (4,7). The answer should be in point slope form.

Algebra ->  Linear-equations -> SOLUTION: What would the equation be for the line that passes throught the points (2,3) and (4,7). The answer should be in point slope form.      Log On


   

Question 101932: What would the equation be for the line that passes throught the points (2,3) and (4,7). The answer should be in point slope form.
Found 2 solutions by checkley75, edjones:
Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
Y=mX+b IS THE LINE FORMULA WHERE m=SLOPE & b=Y INTERCEPT.
FIRST WE FIND THE SLOPE (Y2-Y1)/(X2-X1)
(7-3)/(4-2)=4/2=2 WHICH IS THE SLOPE(m)
NOW USE ONE SET OF X,Y VALUES & SOLE FOR b
3=2*2+b
3=4+b
b=3-4
b=-1 THUS THE LINE EQUATION IS:
Y=2X-1

Answer by edjones(8007) 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 (2,3) and (4,7)


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 (2,3) and (x%5B2%5D,y%5B2%5D) is the second point (4,7))


m=%287-3%29%2F%284-2%29 Plug in y%5B2%5D=7,y%5B1%5D=3,x%5B2%5D=4,x%5B1%5D=2 (these are the coordinates of given points)


m=+4%2F2 Subtract the terms in the numerator 7-3 to get 4. Subtract the terms in the denominator 4-2 to get 2




m=2 Reduce



So the slope is

m=2





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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=%282%29%28x-2%29 Plug in m=2, x%5B1%5D=2, and y%5B1%5D=3 (these values are given)



y-3=2x%2B%282%29%28-2%29 Distribute 2


y-3=2x-4 Multiply 2 and -2 to get -4%2F1. Now reduce -4%2F1 to get -4

y=2x-4%2B3 Add 3 to both sides to isolate y


y=2x-1 Combine like terms -4 and 3 to get -1

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Answer:



So the equation of the line which goes through the points (2,3) and (4,7) is:y=2x-1


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


Notice if we graph the equation y=2x-1 and plot the points (2,3) and (4,7), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=2x-1 through the points (2,3) and (4,7)


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