SOLUTION: Write the equation of the line with x-intercept (12, 0) and y-intercept (0, 4).

Algebra ->  Graphs -> SOLUTION: Write the equation of the line with x-intercept (12, 0) and y-intercept (0, 4).      Log On


   

Question 74619: Write the equation of the line with x-intercept (12, 0) and y-intercept (0, 4).
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To find the equation that goes through (12, 0) and (0, 4) we need to find the slope:
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (12,0) and (0,4)


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 (12,0) and (x%5B2%5D,y%5B2%5D) is the second point (0,4))


m=%284-0%29%2F%280-12%29 Plug in y%5B2%5D=4,y%5B1%5D=0,x%5B2%5D=0,x%5B1%5D=12 (these are the coordinates of given points)


m=+4%2F-12 Subtract the terms in the numerator 4-0 to get 4. Subtract the terms in the denominator 0-12 to get -12




m=-1%2F3 Reduce



So the slope is

m=-1%2F3





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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%2F3%29%28x-12%29 Plug in m=-1%2F3, x%5B1%5D=12, and y%5B1%5D=0 (these values are given)



y-0=%28-1%2F3%29x%2B%28-1%2F3%29%28-12%29 Distribute -1%2F3


y-0=%28-1%2F3%29x%2B4 Multiply -1%2F3 and -12 to get 12%2F3. Now reduce 12%2F3 to get 4

y=%28-1%2F3%29x%2B4%2B0 Add 0 to both sides to isolate y


y=%28-1%2F3%29x%2B4 Combine like terms 4 and 0 to get 4

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Answer:



So the equation of the line which goes through the points (12,0) and (0,4) is:y=%28-1%2F3%29x%2B4


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-1%2F3 and the y-intercept is b=4


Notice if we graph the equation y=%28-1%2F3%29x%2B4 and plot the points (12,0) and (0,4), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%28-1%2F3%29x%2B4 through the points (12,0) and (0,4)


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



So the equation is
y=%28-1%2F3%29x%2B4