SOLUTION: Find the equation of the line that passes through the points (1,-1) and (-2,-7).

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Question 96874This question is from textbook Algebra 2
: Find the equation of the line that passes through the points (1,-1) and (-2,-7). This question is from textbook Algebra 2

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,-1) and (-2,-7)

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,-1) and is the second point (-2,-7))

m=%28-7--1%29%2F%28-2-1%29 Plug in y%5B2%5D=-7,y%5B1%5D=-1,x%5B2%5D=-2,x%5B1%5D=1 (these are the coordinates of given points)

m=+-6%2F-3 Subtract the terms in the numerator -7--1 to get -6. Subtract the terms in the denominator -2-1 to get -3


m=2 Reduce

So the slope is
m=2

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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--1=%282%29%28x-1%29 Plug in m=2, x%5B1%5D=1, and y%5B1%5D=-1 (these values are given)


y%2B1=%282%29%28x-1%29 Rewrite y--1 as y%2B1


y%2B1=2x%2B%282%29%28-1%29 Distribute 2

y%2B1=2x-2 Multiply 2 and -1 to get -2

y=2x-2-1 Subtract 1 from both sides to isolate y

y=2x-3 Combine like terms -2 and -1 to get -3
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Answer:


So the equation of the line which goes through the points (1,-1) and (-2,-7) is:y=2x-3

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

Notice if we graph the equation y=2x-3 and plot the points (1,-1) and (-2,-7), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=2x-3 through the points (1,-1) and (-2,-7)

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