SOLUTION: find an equation of the line containing (-1,6) and (0,-3) and write the result in slope intercept form

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Question 142827: find an equation of the line containing (-1,6) and (0,-3) and write the result in slope intercept form
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First lets find the slope through the points (-1,6) 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: is the first point (-1,6) and is the second point (0,-3))

m=%28-3-6%29%2F%280--1%29 Plug in y%5B2%5D=-3,y%5B1%5D=6,x%5B2%5D=0,x%5B1%5D=-1 (these are the coordinates of given points)

m=+-9%2F1 Subtract the terms in the numerator -3-6 to get -9. Subtract the terms in the denominator 0--1 to get 1


m=-9 Reduce

So the slope is
m=-9

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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 is one of the given points

So lets use the Point-Slope Formula to find the equation of the line

y-6=%28-9%29%28x--1%29 Plug in m=-9, x%5B1%5D=-1, and y%5B1%5D=6 (these values are given)


y-6=%28-9%29%28x%2B1%29 Rewrite x--1 as x%2B1


y-6=-9x%2B%28-9%29%281%29 Distribute -9

y-6=-9x-9 Multiply -9 and 1 to get -9

y=-9x-9%2B6 Add 6 to both sides to isolate y

y=-9x-3 Combine like terms -9 and 6 to get -3 (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 (-1,6) and (0,-3) is:y=-9x-3

The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-9 and the y-intercept is b=-3

Notice if we graph the equation y=-9x-3 and plot the points (-1,6) and (0,-3), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=-9x-3 through the points (-1,6) and (0,-3)

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