SOLUTION: give an equation for the line whose x-intercept is 5 and whose y-intercept is -4

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Question 102093: give an equation for the line whose x-intercept is 5 and whose y-intercept is -4
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
(5,0)(0,-4)
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (5,0) 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 (5,0) and (x%5B2%5D,y%5B2%5D) is the second point (0,-4))


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


m=+-4%2F-5 Subtract the terms in the numerator -4-0 to get -4. Subtract the terms in the denominator 0-5 to get -5




m=4%2F5 Reduce



So the slope is

m=4%2F5





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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=%284%2F5%29%28x-5%29 Plug in m=4%2F5, x%5B1%5D=5, and y%5B1%5D=0 (these values are given)



y-0=%284%2F5%29x%2B%284%2F5%29%28-5%29 Distribute 4%2F5


y-0=%284%2F5%29x-4 Multiply 4%2F5 and -5 to get -20%2F5. Now reduce -20%2F5 to get -4

y=%284%2F5%29x-4%2B0 Add 0 to both sides to isolate y


y=%284%2F5%29x-4 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 (5,0) and (0,-4) is:y=%284%2F5%29x-4


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=4%2F5 and the y-intercept is b=-4


Notice if we graph the equation y=%284%2F5%29x-4 and plot the points (5,0) and (0,-4), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%284%2F5%29x-4 through the points (5,0) and (0,-4)


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