SOLUTION: Write the equation of the line with x-intercept (14, 0) and y-intercept (0, 2).

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Question 82395: Write the equation of the line with x-intercept (14, 0) and y-intercept (0, 2).

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since we know the intercepts, we know two points of the line. So lets fing the equation of the line through (14, 0) and (0, 2).
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (14,0) 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 (14,0) and (x%5B2%5D,y%5B2%5D) is the second point (0,2))


m=%282-0%29%2F%280-14%29 Plug in y%5B2%5D=2,y%5B1%5D=0,x%5B2%5D=0,x%5B1%5D=14 (these are the coordinates of given points)


m=+2%2F-14 Subtract the terms in the numerator 2-0 to get 2. Subtract the terms in the denominator 0-14 to get -14




m=-1%2F7 Reduce



So the slope is

m=-1%2F7





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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-0=%28-1%2F7%29%28x-14%29 Plug in m=-1%2F7, x%5B1%5D=14, and y%5B1%5D=0 (these values are given)



y-0=%28-1%2F7%29x%2B%28-1%2F7%29%28-14%29 Distribute -1%2F7


y-0=%28-1%2F7%29x%2B2 Multiply -1%2F7 and -14 to get 14%2F7. Now reduce 14%2F7 to get 2

y=%28-1%2F7%29x%2B2%2B0 Add 0 to both sides to isolate y


y=%28-1%2F7%29x%2B2 Combine like terms 2 and 0 to get 2

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Answer:



So the equation of the line which goes through the points (14,0) and (0,2) is:y=%28-1%2F7%29x%2B2


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-1%2F7 and the y-intercept is b=2


Notice if we graph the equation y=%28-1%2F7%29x%2B2 and plot the points (14,0) and (0,2), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%28-1%2F7%29x%2B2 through the points (14,0) and (0,2)


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