SOLUTION: Find and equation of the line satisfying the given condition : - Through the two points (-1,-5) and (3,6)

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Question 840530: Find and equation of the line satisfying the given condition :
- Through the two points (-1,-5) and (3,6)
Answer by jim_thompson5910(35256) 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 (-1,-5) and (3,6)


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 (-1,-5) and (x%5B2%5D,y%5B2%5D) is the second point (3,6))


m=%286--5%29%2F%283--1%29 Plug in y%5B2%5D=6,y%5B1%5D=-5,x%5B2%5D=3,x%5B1%5D=-1 (these are the coordinates of given points)


m=+11%2F4 Subtract the terms in the numerator 6--5 to get 11. Subtract the terms in the denominator 3--1 to get 4



So the slope is

m=11%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--5=%2811%2F4%29%28x--1%29 Plug in m=11%2F4, x%5B1%5D=-1, and y%5B1%5D=-5 (these values are given)



y%2B5=%2811%2F4%29%28x--1%29 Rewrite y--5 as y%2B5



y%2B5=%2811%2F4%29%28x%2B1%29 Rewrite x--1 as x%2B1



y%2B5=%2811%2F4%29x%2B%2811%2F4%29%281%29 Distribute 11%2F4


y%2B5=%2811%2F4%29x%2B11%2F4 Multiply 11%2F4 and 1 to get 11%2F4

y=%2811%2F4%29x%2B11%2F4-5 Subtract 5 from both sides to isolate y


y=%2811%2F4%29x-9%2F4 Combine like terms 11%2F4 and -5 to get -9%2F4 (note: if you need help with combining fractions, check out this solver)



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Answer:



So the equation of the line which goes through the points (-1,-5) and (3,6) is:y=%2811%2F4%29x-9%2F4


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=11%2F4 and the y-intercept is b=-9%2F4


Notice if we graph the equation y=%2811%2F4%29x-9%2F4 and plot the points (-1,-5) and (3,6), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%2811%2F4%29x-9%2F4 through the points (-1,-5) and (3,6)


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