SOLUTION: Find an equation of the line passing through the origin and parallel to the line passing through the points (2,8) and (4,12).

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Question 954280: Find an equation of the line passing through the origin and parallel to the line passing through the points (2,8) and (4,12).
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
first,the equation of the line passing through the points (2,8) and (4,12)
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (2,8) and (4,12)


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 (2,8) and (x%5B2%5D,y%5B2%5D) is the second point (4,12))


m=%2812-8%29%2F%284-2%29 Plug in y%5B2%5D=12,y%5B1%5D=8,x%5B2%5D=4,x%5B1%5D=2 (these are the coordinates of given points)


m=+4%2F2 Subtract the terms in the numerator 12-8 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-8=%282%29%28x-2%29 Plug in m=2, x%5B1%5D=2, and y%5B1%5D=8 (these values are given)



y-8=2x%2B%282%29%28-2%29 Distribute 2


y-8=2x-4 Multiply 2 and -2 to get -4%2F1. Now reduce -4%2F1 to get -4

y=2x-4%2B8 Add 8 to both sides to isolate y


y=2x%2B4 Combine like terms -4 and 8 to get 4

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Answer:



So the equation of the line which goes through the points (2,8) and (4,12) is:y=2x%2B4


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=4


Notice if we graph the equation y=2x%2B4 and plot the points (2,8) and (4,12), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=2x%2B4 through the points (2,8) and (4,12)


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




then, the line y=mx%2Bb parallel to line y=2x%2B4 will have same slope m=2 and since passing through origin (0,0, y-intercept b=0
so, equation of the line parallel to line y=2x%2B4 is y=2x