SOLUTION: Find the equation of the line with an x-intercept of 4 and a y-intercept of -3.

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Question 82485: Find the equation of the line with an x-intercept of 4 and a y-intercept of -3.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since we know the intercepts, we know 2 points on the line which are (4,0) and (0,-3)

Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (4,0) and (0,-3)


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 (4,0) and (x%5B2%5D,y%5B2%5D) is the second point (0,-3))


m=%28-3-0%29%2F%280-4%29 Plug in y%5B2%5D=-3,y%5B1%5D=0,x%5B2%5D=0,x%5B1%5D=4 (these are the coordinates of given points)


m=+-3%2F-4 Subtract the terms in the numerator -3-0 to get -3. Subtract the terms in the denominator 0-4 to get -4




m=3%2F4 Reduce



So the slope is

m=3%2F4





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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=%283%2F4%29%28x-4%29 Plug in m=3%2F4, x%5B1%5D=4, and y%5B1%5D=0 (these values are given)



y-0=%283%2F4%29x%2B%283%2F4%29%28-4%29 Distribute 3%2F4


y-0=%283%2F4%29x-3 Multiply 3%2F4 and -4 to get -12%2F4. Now reduce -12%2F4 to get -3

y=%283%2F4%29x-3%2B0 Add 0 to both sides to isolate y


y=%283%2F4%29x-3 Combine like terms -3 and 0 to get -3

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Answer:



So the equation of the line which goes through the points (4,0) and (0,-3) is:y=%283%2F4%29x-3


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=3%2F4 and the y-intercept is b=-3


Notice if we graph the equation y=%283%2F4%29x-3 and plot the points (4,0) and (0,-3), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%283%2F4%29x-3 through the points (4,0) and (0,-3)


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