SOLUTION: (writing linear equations in point slope form) write the point-slope form of an wquation of the line that passes through each pair of points. (-1,-7),(1,3)

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: (writing linear equations in point slope form) write the point-slope form of an wquation of the line that passes through each pair of points. (-1,-7),(1,3)      Log On


   

Question 118262: (writing linear equations in point slope form)
write the point-slope form of an wquation of the line that passes through each pair of points.
(-1,-7),(1,3)
Found 2 solutions by jim_thompson5910, TP:
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,-7) and (1,3)

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,-7) and is the second point (1,3))

m=%283--7%29%2F%281--1%29 Plug in y%5B2%5D=3,y%5B1%5D=-7,x%5B2%5D=1,x%5B1%5D=-1 (these are the coordinates of given points)

m=+10%2F2 Subtract the terms in the numerator 3--7 to get 10. Subtract the terms in the denominator 1--1 to get 2


m=5 Reduce

So the slope is
m=5

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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--7=%285%29%28x--1%29 Plug in m=5, x%5B1%5D=-1, and y%5B1%5D=-7 (these values are given)


y%2B7=%285%29%28x--1%29 Rewrite y--7 as y%2B7


y%2B7=%285%29%28x%2B1%29 Rewrite x--1 as x%2B1


y%2B7=5x%2B%285%29%281%29 Distribute 5

y%2B7=5x%2B5 Multiply 5 and 1 to get 5

y=5x%2B5-7 Subtract 7 from both sides to isolate y

y=5x-2 Combine like terms 5 and -7 to get -2
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Answer:


So the equation of the line which goes through the points (-1,-7) and (1,3) is:y=5x-2

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

Notice if we graph the equation y=5x-2 and plot the points (-1,-7) and (1,3), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=5x-2 through the points (-1,-7) and (1,3)

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

Answer by TP(29) About Me  (Show Source):
You can put this solution on YOUR website!
m(the gradient)=vertical distance between the two points/horizontal distance between the two points.
So m=(Y-y)/(X-x) where the two points have coordinates of (X,Y) and (x,y).
So here (X,Y)=(-1,-7) and (x,y)=(1,3).
Hence the gradient m=(-7-3)/(-1-1)=-10/-2=5.
Now the general equation of a straight line is y=mx+c where m is the gradient and c is the y intercept(the y value where the line crosses the vertical Y axis).
So far we have: y=5x+c.(i)
We need to find the value of c.
Since the line passes through (1,3) then we can replace x and y in our equation by 1 and 3 respectively.
This gives (i) as: 3=5*1+c
So 3=5+c
Subtract 5 from each side of the equation and we get: 3-5=c
So c=-2
Hence the required equation is y=5x-2 ANS
(N.B. You should verify your answer by replacing the x by -1 and the y by -7)