SOLUTION: what is an equation in slope-intercept form for the line containing the point(9,-3)and(0,5)?

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Question 111297: what is an equation in slope-intercept form for the line containing the point(9,-3)and(0,5)?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (9,-3) and (0,5)


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


m=%285--3%29%2F%280-9%29 Plug in y%5B2%5D=5,y%5B1%5D=-3,x%5B2%5D=0,x%5B1%5D=9 (these are the coordinates of given points)


m=+8%2F-9 Subtract the terms in the numerator 5--3 to get 8. Subtract the terms in the denominator 0-9 to get -9




m=-8%2F9 Reduce



So the slope is

m=-8%2F9





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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--3=%28-8%2F9%29%28x-9%29 Plug in m=-8%2F9, x%5B1%5D=9, and y%5B1%5D=-3 (these values are given)



y%2B3=%28-8%2F9%29%28x-9%29 Rewrite y--3 as y%2B3



y%2B3=%28-8%2F9%29x%2B%28-8%2F9%29%28-9%29 Distribute -8%2F9


y%2B3=%28-8%2F9%29x%2B8 Multiply -8%2F9 and -9 to get 72%2F9. Now reduce 72%2F9 to get 8

y=%28-8%2F9%29x%2B8-3 Subtract 3 from both sides to isolate y


y=%28-8%2F9%29x%2B5 Combine like terms 8 and -3 to get 5

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Answer:



So the equation of the line which goes through the points (9,-3) and (0,5) is:y=%28-8%2F9%29x%2B5


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-8%2F9 and the y-intercept is b=5


Notice if we graph the equation y=%28-8%2F9%29x%2B5 and plot the points (9,-3) and (0,5), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%28-8%2F9%29x%2B5 through the points (9,-3) and (0,5)


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