SOLUTION: Could you please help me solve and understand this equation? Find an equation of the line containing the given pairs of points (4,3) and (12,7) Y=

Algebra ->  Linear-equations -> SOLUTION: Could you please help me solve and understand this equation? Find an equation of the line containing the given pairs of points (4,3) and (12,7) Y=      Log On


   

Question 87561: Could you please help me solve and understand this equation?
Find an equation of the line containing the given pairs of points
(4,3) and (12,7) Y=
Found 2 solutions by ankor@dixie-net.com, jim_thompson5910:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Could you please help me solve and understand this equation?
Find an equation of the line containing the given pairs of points
(4,3) and (12,7) Y=
:
There are two formulas that you should know when dealing with slope equations:
:
1st one is the "slope equation": m = %28%28y2-y1%29%29%2F%28%28x2-x1%29%29%29
:
Assign the given coordinates as follows:
x1=4, y1=3, x2=12, y2=7
:
Using the slope equation and these values, find the slope
m = %28%287-3%29%29%2F%28%2812-4%29%29%29 = 4%2F8 = 1%2F2
:
The 2nd formula you should know is the "point/slope equation": y-y1 = m(x-x1)
:
Using the values: m = 1/2 or m = .5; x1=4, y1=3
y - 3 = .5(x - 4)
y - 3 = .5x - 2; multiplied what was in brackets
y = .5x - 2 + 3; added 3 to both sides
y = .5x + 1; is the equation derived from the given coordinates
:
You can always check the equation by substituting the value for x and seeing if the gives you the given value for y:
Using x=4 and y = 3
y = .5(4) + 1
y = 2 + 1
y = 3
:
You can do the same with the 2nd set of coordinates.
Using x = 12, y = 7
y = .5(12) + 1
y = 6 + 1
y = 7
:
I tried to explain this step by step, let me know if it helped you understand it.

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 (4,3) and (12,7)


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 (4,3) and (x%5B2%5D,y%5B2%5D) is the second point (12,7))


m=%287-3%29%2F%2812-4%29 Plug in y%5B2%5D=7,y%5B1%5D=3,x%5B2%5D=12,x%5B1%5D=4 (these are the coordinates of given points)


m=+4%2F8 Subtract the terms in the numerator 7-3 to get 4. Subtract the terms in the denominator 12-4 to get 8




m=1%2F2 Reduce



So the slope is

m=1%2F2





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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=%281%2F2%29%28x-4%29 Plug in m=1%2F2, x%5B1%5D=4, and y%5B1%5D=3 (these values are given)



y-3=%281%2F2%29x%2B%281%2F2%29%28-4%29 Distribute 1%2F2


y-3=%281%2F2%29x-2 Multiply 1%2F2 and -4 to get -4%2F2. Now reduce -4%2F2 to get -2

y=%281%2F2%29x-2%2B3 Add 3 to both sides to isolate y


y=%281%2F2%29x%2B1 Combine like terms -2 and 3 to get 1

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Answer:



So the equation of the line which goes through the points (4,3) and (12,7) is:y=%281%2F2%29x%2B1


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=1%2F2 and the y-intercept is b=1


Notice if we graph the equation y=%281%2F2%29x%2B1 and plot the points (4,3) and (12,7), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%281%2F2%29x%2B1 through the points (4,3) and (12,7)


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